Ah, sure - timeblazer stands in its own little world since minigames aren't a diversion from the action, they are the action. But I was asking about something more like Booster Hill in Super Mario RPG or the parade marching in FF7 where you just play it once as part of the plot (and in some cases can choose to play it again later) - and it sounds like you still tend to dislike these, which is suprising to me but a totally reasonable opinion.
See, I grew up on the 80's adventure games where developers loved to pad the games by adding mandatory mini games that if you could not pass them, you couldn't advance. I was stuck on some games for 2 - 3 years as I couldn't beat that $%#^& space shooter minigame (Space Quest 3, I'm looking at you!).
Classic examples of this used badly in the 80's (all adventure games):
Police Quest 1: Must beat a poker minigame 2x to advance the plot.
Space Quest 1: Must win the land rover minigame or else you cannot advance. Then, once you win that, you must win 250 coins in a slot machine or you cannot advance.
Space Quest 3: Must win a robot punch out minigame, then a space shooter minigame to win the game.
So I think due to those games (and a few others) I grew to hate minigames by the time I was 12. Thankfully most RPG's I've played didn't go down the mandatory route, else I would probably have never grown to like RPG's.
I hate that almost as much as requiring certain side quest clear percentages to proceed in the main quest.
THIS. If you are going to do this that makes the side quests mandatory. Just call them a main quest then.