Besides they're usually badly implemented and not fun. If a mini game becomes a chore, it gets annoying pretty quickly.
the "badly implemented and not fun" part probably the most important point when it come to mini-games.
There's a game I'll not name, that I finally decided to test recently. For one job, you need to press keys when they appear on screen. It's a classical, not really difficult to do, nor to play. While it's a bit boring, it's basic enough to not displease too much.
But the first cons is that you need to play it to earn some money, while you need to spend this money before the story effectively starts.
From memory, I earned 40, while you need around 2.260 at all. Playing it 3 or 4 times is enough to unlock the second job, that also rely on a mini-game. I don't know how you can earn with it, nor even what it is, I gave me +5.000 when I saw that it was also a min-game.
The reward is too small in regard of the expenses the MC have to do. The player will have to pass most of his time waiting for the possibility to play the mini-game, while waiting to have finally played it long enough to finally advance on the story. This reverse the natural order of the main game, putting the mini-games in the first place, while they should be a complement of the story.
People will play your game for either its story or the lewd content. If they wanted to have some challenge, they would play one of the thousands "regular games", and if they wanted entertaining mini-games, it's one of the hundreds of thousands mobile games that they would have chosen. Therefore, the mini-game should never take the first place in your game, and even less block the player for a so long time.
The second cons is the key needed to play it: J B Y C.
They aren't at all well placed. You can't have a finger on each with just one hand, and without one hand over lapsing the other. And the fingers that will be on the keys aren't the good ones.
To be natural, either it's a one hand configuration (like the arrow keys, or the IJKL that served as second player for years), or the two hands should be effectively apart, and you can use the index for one key, and the major for the second (XC and IO by example).
The third cons is the general look of the mini-games.
I don't remember well how it looks, but it wasn't really engaging. A mini-game like that should have letters that stand out on the screen (big size and high contrast), here it was more blended on the screen and too small.
And obviously, the fourth cons is that the alternative you have is yet another mini-game.