I'm kinda intrigued by the OP scenario: -- someone wanted the most realistic thing they could, but that challenge became self-defeating in spots; then they wanted things balanced and able to prevent optimization-seeking power-players. This is interesting because game balance is usually framed as opposed to fitting iconic roles or fun; and realism is usually framed as opposed to playability (no one wants the 1-10 second rounds to take 10-20 minutes to resolve), or even whether realism was a primary goal (the old 'I don't care that you have X00 hours of training with Y and want to tell me how fiction Z gets them wrong, I came here to play a game which emulates fiction Z because it is cooler than real life').
I think the first issue is a semi-universal experience -- someone wants to design a system, wants something realistic, finds a downstream consequence (either impacting realism or balance), makes change, finds a consequence, and so on. Certainly I've seen lots of time spent hyperfocused on finer details, only to see any value wiped away by overall system conceits. Those can be as specific as the game doesn't have weapon reach or wearability/draw rules*, or as broad as your system being one (like most RPGs) where each person acts on their turn and then freezes in place while the next person acts**--which by itself can dwarf all the effort you might make in having the combat play out realistically.
*or whatever else makes spears or shortswords preferable to longswords
**with some exceptions such as reserved APs or reactions or abort-to-dodge
I always like to say realism isn't my primary concern it's versimilitude. I don't want to spend 5 minutes each time a PC decides to fire a burst of automatic fire from his Thompson submachine gun to see how many hit the target, where they hit the target, and what kind of damage it does to the target.
Automatic weapons are a key example -- realistically, automatic weapons are often (in interpersonal warfare) used as suppression, yet lots of systems either don't have such rules, or the rules are such that it is mechanically preferable to use it just as a normal weapon, but with a lot more attack rolls. This and the above situation (rules don't exist which highlight the IRL benefits or limits of an option) lead to situations like (IIRC, it's been a while) Shadowrun 1E where everyone either used submachine guns for maximum ROF or sniper rifles (for maximum damage, since all the reasons you don't bring a long-barrel rifle to aback-alley fights weren't in the ruleset).
The second part -- someone finds an exploit in the 'realistic' rules that becomes immanently exploitable-- seems to happen (or at least is more likely to make it to the finished product) whenever not doing so isn't a high priority (when realism, role, fun, and/or narrative priorities take the for). One of the reasons why it's sometimes important to consider whether perfect balance is even the goal. However, when someone finds an 'always best option' exploit/choice like the OP's character with the most action points, it's usually getting in the way of role, fun, and narrative focus as well as balance.
In such a case, you can either 1. (as OP suggested) include some kind of 'artificial' balancing metric, or 2. recognize that realistically, one given thing is rarely always best in all cases, and if the so-called realistic optimal choice probably isn't just realistically favored, but also favored by selective advantage in the mechanistic benefit chosen to represent this real-world trait. Continuing with the OP example--quicker reflexes and being able to
do more in a given time is, realistically, a huge benefit. However, having situational knowledge, and thus spending your actions only on things which
actually help achieve your goal is also a huge advantage (Speedy McFasterthanyou can be just as doomed as anyone else if he barrels into a room and starts shredding enemies, but walked right by the guy behind the door who is now lining up a shot...). If the 'realistic' game favors Action Points, but doesn't favor awareness (and many games unrealistically treat combatants as knowing about any non-hidden thing in the battle scene), well then it isn't really more realistic (it's just favoring a strategy/rule-component with a realism justification).
Most superhero games intentionally nerf superspeed and overprice the nerfed version because it’s just a fancy I win button. It’s either that or everyone’s a speedster and you have a dull game.
This would be an example of the above. In the cases of comics DC Flash and Sony-version Marvel Quicksilver (who in effect lives in a world of near-frozen people), this is reasonable, but then those powers should be super high in build-component cost. MCU Quicksilver is a good example of how it could work out counter to this -- super speed might mean you can outrun bullets, but not so fast that you can deflect them out of their trajectory towards your friends (so that your only option is taking the bullets for them), and no specific benefit for noticing all the things you need to use your speed to take care of. Super speed could also only mean more actions (including action points spent on defense rolls, if that's a thing in your game), but not auto-dodge nor auto-armor-pierce. So Flash gets an attack on each opponent and a dodge on each opponent but Bullseye gets their one shot back on him and has such a high to-hit that the dodge-action they have isn't sufficient (hope Flash has some HP as well), or they can take 50 attack actions against Collossus, but none of them penetrate, and then Marvel Girl grabs him with telekinesis and they take turns slamming him into things. Maybe his speed is so great that he can dodge everything his opponents can do, and run fast enough to overpower the telekinesis, and has so much time between clock-second-tics that of course he's going to notice the important things; but that's moving back to a strategy-favoring set of mechanics (with a realism justification) someone decided had to be the one to represent a speedster.
DnD has it's own version of this, limiting spell users to keep them from dominating a group.
This seems like kind of an outlier to the scenario. Yes, magic has the per-day limits as a means of keeping casters and non-casters playable together. However, there isn't a realistic way that spellcasting is supposed to work. I don't think I can say that it is an 'artificial' limit. The spellcaster who could cast infinite 1-round-casting-time, battlefield-convenient, no-other-cost spells; who needed to be nerfed for balance reasons; wasn't otherwise on the table. Most iconic images of casters have additional limits which would keep them out of dungeoncrawls -- They are one-of-a-king demigodlike beings whose primary concerns are getting rings to Mount Doom or King Arthur on the throne; their spells take days of incantations and ritual chanting by them and their closest dozen cultist friends; you are a ten thousand year old sorcerer whose life force is protectected by a fist-sized jewel Conan and the priests of Mitra keep trying to steel and destroy; all spells are deals with minor spirits and each one has a cost in life-force (or just tasks you agree to do); etc. There is no specific reason that there would be an limitless caster interested in adventuring with knights and priests and thieves that is only receiving these X/day limitations as a form of balance. Instead the D&D casters are built from the ground with both the conveniences they have and the limits they have both to facilitate their role alongside non-casters. It is still a limitation made for balance, but I guess I just don't see it as a good parallel to mechanisms or build which 'realistically' should dominate but games don't let them for balance concerns.