Increased characterization will provide interesting theoretical optimization challenges, reduce the strategic options of the DM, and make it more likely for you to actually play a game session.

I'm actually going to expand the question slightly:

What are the benefits of increased characterization?

As stated, any attempt at characterization theoretically creates more in-world reasons for the DM to attack you. Be it a character goal, alignment, or what have you.

We must address three things: The opportunity cost of characterization to the DM, the opportunity cost to the player, and the benefits to the player. In many ways, I will be drawing on my character optimization paper here.

What it allows the DM to do and not do

An alignment, or characterization, allows the DM to structure the world and opponents to more closely align with the character's goals. If the character is a good character desiring power, a kindly (but not too deep) DM will present evil opponents inhabiting the world to provide a guilt-free slaying experience, because that is, apparently, what good people do in D&D.

But, more to the point for an optimizer, it constrains the DM's decision space. Given that the DM can place any enchantment on a monster and that consecrate and the various $antiAlignment spells exist, a monster who takes those spells cannot take others. Given that you know the more likely set of spells taken/enchanted by monsters, it becomes trivial to then prevent those spells from providing any utility to the DM through strategically chosen counter-spells.

To summarize: characterization choices you make restrict the "logical" (in terms of story) courses of action the DM is likely to take, making it easier to foil those courses of action. Given the non-optimal nature of anti-alignment spells and effects, you can entice the DM into sub-optimal "play" through increased characterization.

Opportunity costs to the player

The act of characteriazation, be it through alignments or a more nuanced moral code, is the act of articulating and playing a series of prescriptions and proscriptions: acts that you would prefer to do and not do. Theoretically speaking, this absolutely limits the gross decision space of possible actions you may take. However, the addition of structure via pre- and pro-scriptions into your decision space allows for more nuanced choices, strategies, and options.

Structure, while nominally forbidding actions, creates a logical framework that improve the coherency of the action space as a whole, while allowing "forbidden" actions, through an act of reframing, to both be allowed and character-affirming.

Benefits to the player

As an optimizer, but as someone who enjoys RP, there is an interesting dichotomy in play. The problem I all-too-often finding myself having is weighing otherwise equal mechanical choices. By creating a narrative framework and narrative requirements, I find that certain choices by their appropriateness to the narrative, become more attractive.

Though, while looking at your bio, I found this:

I like to optimise my characters for maximum efficiency, but unfortunately I’ve done this to the point where no one will GM for me anymore :(

The best benefit of characterization, and the best benefit of choosing alignments to support a narrative structure is: people will be more interested in playing with/DMing for you.

A theoretical character that can theoretically beat Pun-Pun a level before he hatches is all well and good, but it still lacks the necessary social prerequisites that transform it from a fascinating mathematical exercise into a game. By intentionally creating restrictions and requirements for your characters, you can present yourself with a greater optimization challenge (which I personally find more fun then bland already-solved puzzles of max damage), and allow for opportunities to bring these theoretical abstractions into play.

Edit (based on reflection):

Weakness is a poorly framed statement.

I’m a power gamer at heart, and I cannot bring myself to play characters with weaknesses. The only time I will consider playing anything other than TN is when I’m rolling a Paladin.

This statement, more than anything, is a framing problem(caution, SEP). As alignment is representative of characterization, and you view characterization as a threat to optimization, you can then weight your ontological values placed on the (trivially counterable magics and items) such that they prohibit you from making any other choice than the one you just made.

Asking you to update your fundamental belief system based on an answer is silly. And while I (think I) make persuasive comments above vis-a-vis characterization, if you don't want to do it, you don't have to.

Here is some logic to reduce your confidence in your belief of true neutral's superiority:

1. Given: you wish to play as a "power gamer" which is nominally expressed as:
   1. "I want to be able to express maximum arbitrary agency upon the world while preventing the world from expressing its will upon me."
   2. Translation: I want to do the most damage while taking the least damage.
2. You will therefore always play Tier 1 classes. The impact in capability between tier 1 and tier 2 is such that, according to the value system above, you will never choose tier 2.
   1. Given a tier 1 class, we must then ask if the resources required to negate an alignment-based attack displace resources that would otherwise be used to negate other expressions of GM agency.
      1. Primus: Given magic weapons, a competent Tier 1 character will ensure that they are never hit, that they have ablative meat around to take hits, and whatever hits they do take are minizmied.
      2. Therefore, a series of spells will always be active, as a function of level. The character, cognizant of the GM's ability to create foes tailored for her doom, will always have sufficient ability to counterspell or otherwise negate incoming spells, reducing the odds of harmful spells dispelling buffs save for DM fiat.
      3. This structure of defensive spells is necessary to protect against all debuffs, not least "mage-bane" and therefore the secondary, highly-specialized anti-alignment weapons are rendered moot. A dispel magic (or equivalent) can also render them pointless for whatever time is necessary to perminantly correct the problem.
   2. Therefore, incoming magical item based attacks are of no concern to a properly optimized character, even ignoring the ability to pun-pun at level 1-4 (depending).
   3. The ability to use alignment-restricted items is a function of Use Magic Device, and therefore does not impede a character's choices.
   4. Our final concern is incoming spells that use alignment descriptors.
      1. Again, our competent Tier 1 character will have a selection of powers to negate "bothersome" incoming spells and powers.
      2. We care about two spells, primarily:
         1. Blasphemy which can daze-kill non-shared alignment creatures
         2. Unholy Aura which presents SR 25 against good creatures.
      3. Given that Good creatures are willing to be persuaded to a different degree that evil creatures are not.
         1. Given that we have sufficient anti-detection spells up for the persuasiveness of our message not to be impacted by alignment detection
         2. Given sufficiently high Diplomacy to trivially persuade any non-insane creature to your side
         3. See also: Spaceballs.
      4. It is therefore likely that the most common alignment spells that you should worry about are evil-based.
         1. Using this logic, it is better to be Evil than Neutral, as Good can be reasoned with.
            1. Using adequate disguises, your "good" persona should never be connected to the persona that performs evil acts.
            2. Good creatures should be willing to accept surrender. Given that you can talk your way out of anything, surrender is always preferable to a fight you cannot win or walk away from.
         2. Evil does not need to be stupid, and can choose to cooperate with good for its own benefit.
3. Therefore: The correct choice based on the logical structures above is to play an Evil spellcaster (or Tier 1 psion) that has sufficient Diplomacy and Disguise to appear good. The alignment-based concerns of characters that are likely to attack you are completely negated, and the good characters that would otherwise attack you are rendered moot via dialog.
4. Therefore, given sufficient preparation, alignment based spells, SR, and items are all trivially negatable within a necessary defensive framework.
5. Therefore: you may choose to characterize your character without fear that it will impact on your in-game optimization.

Necromancy is not inherently evil

Necromancy spells are only characterized by their use of negative energy; negative energy is entropic in nature but is not a moral force. The inflict line of spells, for example, aren't evil.

But...

Necromancy does have some evil spells. Thankfully, they'll helpfully be labeled [Evil] in the spell descriptions!

Spells associated with particular alignments are indicated by the chaotic, evil, good, and lawful descriptors in their spell descriptions.

Per the Cleric class description, the Cleric cannot use spells with an alignment component opposed to their own; Good Clerics can't use [Evil] spells, Evil Clerics can't use [Good] ones. When in doubt, just check the spell's description!

Further, Channel Energy does not affect non-spontaneous spellcasting. While Channel Energy determines what spells a Cleric may cast without preparing, it doesn't affect spells that the Cleric memorizes ahead of time and does not otherwise restrict their casting list, though their alignment may do so (see above).