This is quite possibly the sort of problem that most people don't have, based on how popular Twitter is and continues to be - and actually that's fantastic. I've seen some really cool grassroots stuff happen due to Twitter linkages, spur-of-the-moment concerts or performance art 'happenings' (yeah, I'm stuck in the last century for terminology, so sue me) and I have nothing but praise to offer for that aspect of the phenomenon.
But for me, little old introvert, doesn't trust or make friends easily me, it was just too disconcerting to be suddenly privy to intimate tidbits of people's lives of the sort I'm only used to from people who want to hear my life-stuff back, without being able to make that reverse connection. Now the nature of the beast is that Twitter is a broadcast medium: you send out your tweet/message, and anyone who wishes, for the most part (unless you act to block them) can receive it. A dialog will only be allowed, however, if you take pains to initiate it or indicate that a particular user has the appropriate permissions. So what you can end up with especially with the famous is a conversation between people who know each other in front of a large audience - almost like a panel discussion - except it tends to be about the mundane (grape jelly, or marmalade?) as often if not moreso than the profound.
As I said, since I have an ego that presumes my answer to any question is at least as good as any other, if not on the better-than-most side. Neil Gaiman, for example, someone I admire, like and respect a great deal, was someone whose Twitter feed I received. And the opportunity to help someone as cool as I think Neil Gaiman is with even a trivial problem is something I would find really satisfying, something I could think about on the crappy days when nothing goes right and I'm wishing they would let you donate your organs early under a euthanasia program. So when in the course of human events Gaiman or someone like him tweets regarding some question or snafu or something that I have knowledge about or think I could help with, I want to offer that help.
Except it would be totally inappropriate, because he's not really talking to me. He doesn't know me, except as a random fan; I have no right to presume I know how to solve problems he has based on the scraps of information I've gleaned as a random fan because despite what it seems like, I don't really know him! Then for me to feel snubbed because of this lack of interaction? That's heading down the lane to psychosis ala the John Hinkley/Jodie Foster/Ronald Regan triangle and I'd really prefer not to go there.
I'll stick to getting text messages from robots or people I actually know, for now, I think.