Non-stealth games put in stealth minigames for the same reason that we put in lockpicking minigames, crafting minigames, rhythm minigames, collectible card minigames, and the others. The entire reason we put them in isn't because they're super fun, but because they provide a breather from the regular gameplay and allow player minds to reset a bit and change things up so players don't get fatigued from too much gameplay repetition.

Our brains are hard wired to get fatigued from doing the same tasks over and over again. We see this in sound effects we hear, in things that we see, in actions that we perform. In games we try to mix the gameplay up so that too much of the core gameplay doesn't fatigue the player. We do this by sprinkling in other tasks to break it up a bit - UI manipulation to equip something new, leveling up interface to do other things, conversations, mini games, cinematics, and so on. They can sometimes be really fun, but that isn't their primary purpose - it's just something for players to do so they don't get tired of playing the rest of the game.

Stealth doesn't tend to work super well as a mini-game - there's so much context to stealth and awareness that humans are intimately familiar with it, so most implementations of stealth tend to be very expensive in order to try simulating that kind of behavior. Because of how costly it is to try to build it properly, most budget stealth implementations generally devolves into some version of red light/green light.
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