The Keen senses option is indeed inherently weaker
Your analysis regarding the Keen senses is correct - it gives you proficiency in a single particular skill when you could have proficiency in two skills of your choice. This issue is known yet uncorrected: In a 2015 tweet DnD 5e's lead rules developer Jeremy Crawford acknowledges it as follows:
The half-elf's Keen Senses option in the SCAG is, alas, superfluous. Take one of the juicy options below it.
This confirms that it indeed is an "or", not an "and".
The most recent errata for Player's Handbook and SCAG contain no mention on changing these rules, so until further revisions you can treat taking Keen senses instead of the Skill versatility as a valid, if nonsensical option of the game.
They can take any race-restricted character option
As pointed out in this answer, in Pathfinder, most half-breeds of humans are also treated members of both parent races, and thus, also treated as humans. This rule extends to:
Orc Blood: Half-orcs count as both humans and orcs for any effect related to race.
Elf Blood: Half-elves count as both elves and humans for any effect related to race.
- Aasimars with Scion of Humanity racial trait:
Scion of Humanity: Some aasimars’ heavenly ancestry is extremely distant. An aasimar with this racial trait counts as an outsider (native) and a humanoid (human) for any effect related to race, including feat prerequisites and spells that affect humanoids.
Such a tiefling doesn’t need to succeed at a Disguise check to appear to be human and count as humanoid (human) as well as outsider (native) for all purposes (such as humanoid-affecting spells like charm person or enlarge person).
Such geniekin appear to be human, save perhaps minor features like unusual eye color, and they count as humanoid (human) as well as outsider (native) for all purposes (such as humanoid-affecting spells such as charm person or enlarge person).
Fetchlings with this racial trait count as outsiders with the native subtype and humanoids with the human subtype for any effect related to race, including feat prerequisites and spells that affect humanoids.
You count as both human and your race for the purpose of taking character options, such as archetypes, feats, spells, traits, and prestige classes.
Keep in mind that planar half-breeds exist for non-human races, as pointed out in Blood of Angels (Aasimars) and Blood of Fiends (Tiefling). Such variants would be an exception to this, as pointed out on the sidebar of Blood of Angels, for instance:
Non-human aasimars have the same statistics as human aasimars with the exception of size. Thus a halfling aasimar is Small but otherwise possesses the same statistics and abilities as a human aasimar-the difference is purely cosmetic. Non-human aasimars do not possess any of the racial abilities of their base race. However, they are usually raised in the same cultural context as other members of their base race, and thus generally adopt the same fighting style as their peers, use the same types of weapons and armor, and study the same skills.
So from a rules-as-written perspective, an Aasimar that has an elf parent and takes Scion of Humanity would count as humanoid(native) and still count also as humanoid(human) instead of humanoid(elf).
But are also affected by any race-specific effects
This may sound strong, but keep in mind that this also affects race-specific effects or effects based on creature type, like the Bane special weapon property, or an Intelligent Magic Item that wishes to defeat/slay all members of a specific race.
A half-orc, for example, is both a humanoid(orc) and a humanoid(human) creature. Meaning that they are affected by both a Human-Bane weapon and a Orc-Bane weapon (luckily, bane doesn't stack). A half-elf would meet the requirements of crafting a Cloak of Elvenkind. And so on.
Best Answer
There are no written mechanics for doing this after character creation.
Unfortunately, there aren't any mechanics (even optional ones) which allow for rearranging the racial ASI after character creation. Tasha's Cauldron of Everything introduced guidance for rearranging racial ASIs during character creation, but is explicit that the guidance is to be applied at 1st level only (Customizing Your Origin, “Ability Score Increases”).
I usually allow my players to do this anyway.
As you play a character through a campaign, it is not at all uncommon for your playstyle to change as you progress. Several times I have had this idea for a character build, and then later decided it really wasn't what I wanted after all. When this happens to my players, I'm pretty generous about allowing them to re-spec their characters - after all, we both want you to have the most fun possible, and if we can make a small change that increases your satisfaction without harming anyone else's, let's make that change. So as a player, just have a conversation with your DM. "Hey DM, so someone else helped me make my character, and as I am learning the game, I am learning what sort of playstyle suits me, I would like to make this attribute score switch that better suits the playstyle I now know I like." I imagine any reasonable DM wouldn't hesitate to let you make that change in this context.
The only time I have vetoed this suggestion was when I felt like a player was taking advantage of my generosity and trying to make situationally beneficial changes to his attribute score distribution. I let him rearrange his attributes during one of the campaign arcs, that made him better suited for the types of enemies I was using, and then he suggested making a similarly beneficial change during another arc that involved a different enemy theme.