I've found that when I don't want a response I can file a bug report or send an email. When I do I can publicly whine on twitter and @-someone.
It sorta feels bad to do but it really does work.
The use case I'd like to use twitter for is trying out some jokes/"deep thoughts", but I don't have enough followers so I just tweet them to the wind and I'll never how just how unfunny I really am. I can definitely understand why most people would use it as a follow-only service - it's somewhat depressing to knowingly broadcast to (almost) nobody.
[1] Wow that's been a word for at least five years. I guess that's not too surprising...