Well said ... however you run into the issue I discussed above.
Answering your assertions in a slightly different order than you make them, while this is inevitably true, I find it is less true of dividing the game into minigames than in games that try to offer single overarching mechanics.
The reason I bring this up isn't to throw cold water on your preferences- I enjoy these types of games as well! Just to point out that the accretion of subsystems has its own particular issues.
It does but in practice what you end up with is that each session you are playing or focusing on the play of what is effectively a different game modelling the same universe. And, aside from the games that are core to that tables play, these sessions will be rare but welcome breaks from the core game play. For example, the core gameplay might be tactical combat and exploration of setting, but every once in a while that game is put on hold while the characters become captains in a mass combat game maneuvering armies over the field. While the rules of this minigame may be different than what they are used to, they can put down the mental apparatus of one minigame while picking up the other one.
The trick is getting these minigames right, which I think is the hardest aspect of this approach. Often this approach leads to tacked on and poorly thought out minigames that are either not engrossing in their own right or spoil the core game in some way such as by leading to even greater absurdities in the simulated reality.
Eventually, you end up with a morass of minigames with different rules.
Absolutely. You will end up with a much fatter game system. But no one session or portion of session will need to depend on the whole rules. And while there is a problem with massive amounts of text and needing to lookup rules in play, IME, this is less of a problem than having no guidance and needing to make up rules in play or attempting to fit a minigame to a situation it doesn't handle (thus discouraging the players from interacting with the fiction) or attempting to have a single more complex set of rules with as few abstractions as possible.
Which leads to the second problem- while this works great in theory, in practice people will have trouble defining the edges of these minigames. If you have a "chase" minigame and a "combat" minigame, what happens when someone wants to shoot an arrow at their pursuer (combat while there is a chase).
This is usually not a problem. Combat within a chase is usually a defined step of the chase and can use a subset of the standard combat rules since the main thing that has changed is not the combat but the movement.
If there is a chase minigame going on, and someone wants to use a general spell, how is that adjudicated?
At least in D&D, the fact that spellcasters find that they often have to fall out of (or fall back in) a chase in order to cast a spell does not prove to be a balance issue, as D&D and many systems need ways to balance mundane skill with the spellcasters power to control the narrative as an act of will. And if your system didn't need to do that, then either you should have thought about it or if you did probably casting a spell is just a different color of standard action.
The bigger problem is probably that when you have a lot of minigames, you have these inelegant transitions between them. Do duels work different than group tactical combat - maybe because you really want to have a quickdraw minigame for your Old West inspired RPG or some such? Do chases work different than either? If they do, then the GM has to declare which sort of rules are in effect in this scene. The metagame needs to intrude into the play, in the way that for example, in Exile III you could manipulate the game by deciding when to switch between the combat minigame and the exploration minigame. Handling those transitions becomes a GM problem.
But again, IME that's still a better problem to have than trying to run a chase scene without rules suited to it, or not having a way to run ship combat in a setting that implies the need for it, or not having strong guidelines for adventures based on social interaction, or having stealth and movement rules that work only for time period measured in combat rounds, or having crafting minigames that are unbalanced (powerful magic items are too cheap to manufacture, or trade goods can be created much more cheaply than standard prices allow), and on and on. Because all of that becomes headaches that the GM has to manage, usually by adopting complex and unwritten processes of play or by attempting to tack on house rules themselves to fill in the gaps.