I had experience with this kind of playstyle back in DnD 3.5. In our case the main problem was that in the first few levels, we went through an incredibly high amount of characters (one of the players had 5 in one session :) ) and this created some monsters in the end (one character had 18,17,16,16 and two stats above 12 in the end) and when you end up with something good, you will start to become increasingly wary and paranoid.

Being wary is not necessary a bad thing, though, and I enjoyed playing in a group where all of our battles were carefully planed out involving crazy traps, potions, and other limited use magic items (which we barely use in more recent systems).

Things that you should be very careful of include:

A bit later in the adventure we started to create characters with very boring and stereotypical backgrounds (as they will die soon anyway). So if you want REAL characters you might want to ask them for example to make up one interesting fact about their character and work that thing out later in the game (one character might be the son of a pirate and later in the game you can introduce some NPCs that support this statement, pirate hunters looking for his dad, other pirates looking for his treasure etc.) This is what we used eventually with limited success.

You should also keep in mind that the players of really bad characters may deliberately try to kill their character so they can roll a better one (maybe even going so far as to get themselves killed 5 times in one session). You can circumvent that with a rule that lets you reroll a character if it is COMPLETELY terrible or one that punishes character death somehow (but I would avoid things like that without the full consent of the players).

How this will affect the game and your players otherwise

• In our game, we almost exclusively played humans because of the random nature of the style and the flexibility of the race. And always picked tier one spell casters if we had the stats to support them (we were relatively lucky because the insanely statted character I mentioned earlier was a dwarf cleric, so healing and tanking was mostly covered just by him; it was also if I remember correctly only his 3rd character).
• We played until 5-6 level so I can’t say too much about higher level play, but extrapolating, I see a very optimized party that blasts through encounters with ease, but is still afraid to attack two goblins without a plan, which really slows down the game (it was one of the reasons why we stopped playing).
• This style can also put pressure at your players because if the party is already at a decent level and nicely statted, mistakes that risk a TPK will meet with harsh anger even from mild tempered players (the other reason why we stopped).

With my experience I would not recommend this playstyle to anyone, but if your players are all into it, it can be fun for a time.

These are approximately equivalent.

2 Skill proficiencies are more useful than a language overall (both in my experience and according to the rulebook in so far as you can train languages, but not skills, with the Downtime rules in the Player's Handbook), so you have to be careful, but losing your choice of a cantrip for one of the least useful ones (in my experience) should account for this discrepancy.

This can also be seen by comparing the Half-Elf and High Elf racial traits side by side (as these official races are roughly balanced with each other).

">" is slightly better than; ">>" is noticeably better than; ">>>" is much better than

\begin{array}{rcl} \bf\text{High Elf} & & \bf\text{Half-Elf} \\ \hline \text{+2/+1 ASI} & \text{<<} & \text{+2/+1/+1 ASI}\\ \hline \text{Fey Ancestry} & \text{=} & \text{Fey Ancestry} \\ \hline \text{Darkvision} & \text{=} & \text{Darkvision}\\ \hline \text{Extra Language} & \text{=} & \text{Included}\\ \hline \text{Keen Senses} & \text{≈} & \text{1/2 Skill Versatility}\\ \hline \text{Cantrip} & \text{>} & \text{1/2 Skill Versatility}\\ \hline \text{Trance} & \text{>} & \text{none}\\ \hline \text{Elf Weapon Training} & \text{≈} & \text{none}\\ \hline \end{array}

I consider Keen Senses and "skill of your choice" to be roughly equivalent since Perception is one of the more useful skills available from experience and WoTC Adventure Module analysis. Elf Weapon Training is a very minuscule benefit.

Now let's take your Sun Elf Homebrew and compare it in the same manner.

\begin{array}{rcl} \bf\text{Sun Elf} & & \bf\text{Half-Elf} \\ \hline \text{+2/+1 ASI} & \text{<<} & \text{+2/+1/+1 ASI}\\ \hline \text{Fey Ancestry} & \text{=} & \text{Fey Ancestry} \\ \hline \text{none} & \text{<} & \text{Darkvision}\\ \hline \text{none} & \text{≈} & \text{+1 Language}\\ \hline \text{Noble Heritage} & \text{<} & \text{Skill Versatility}\\ \hline \text{knows } light & \text{>} & \text{none}\\ \hline \text{Trance} & \text{>} & \text{none}\\ \hline \text{Elf Weapon Training} & \text{≈} & \text{none}\\ \hline \text{Celestial Resistance} & \text{>>} & \text{none}\\ \hline \end{array}

This hinges on the fact that Necrotic and Radiant are rarer damage types in your setting and that History and Persuasion are not used more often in your campaign. In a setting with heavy intrigue and/or many creatures that deal Necrotic or Radiant damage, this race may be unbalanced as Celestial Resistance is pushed to much better than status and/or Noble Heritage is roughly equivalent to Skill Versatility (I've not done any analysis on the proportion of campaign-styles where this is relevant like the WoTC balance team likely did, so I can't say for sure if this is balanced overall, but it seems to be).