Part of this syndrome is that we're all too polite to say what we really want, because we've been brought up that way. Many of us have been brought up with the idea that it's rude to be direct, or to say "I want". And the fault is sometimes with the asker, as well as the IDMer.
A related problem is when people agree to anything and everything, and then seethe about it. That's just as bad as falsely saying IDM in my book, but again it might be someone's upbringing. With my DH, if I agreed to do something onerous, and followed through, he'd sometimes say guiltily "are you sure you don't mind doing this?". I would reply "You know my rule, I won't agree to do something if I'm not prepared to follow it through". And if I do something under duress, I make my displeasure plain. Also, the phrase "would you mind" is often used when there isn't really a choice, e.g. "would you mind emptying the dishwasher?".
I'm sure some people reading this thread are smirking because they have the opposite problem: everyone wants to decide!
"Where shall we go today?" If we really mean "help me decide", we should say so. Perhaps we could all say "your turn to decide this time" first.
As for "I don't mind" itself: if I hear this as a reply, I take people at their word. If they don't like what they get, tough. I sometimes say with indecisive people "We'll do XYZ; if you don't like it, speak now, or for ever hold your peace."