> Why do you assume you're someone worth having a random conversation with at all?
...
> On the rare times I've tried to engage people in conversation they react like I would: impatience that I'm wasting their time, and/or blank looks.
> I'd really discourage anyone trying to randomly engage people in conversation unless you're sure you really have some kind of shared interest.
In my experience, the conversations are almost always very positive. Others report positive experiences and find it worthwhile. That suggests you are sadly missing something. The odd thing is, you seem to want to stop others from having these positive experiences.
I reject any question about my worth or anyone's 'worth'. Perhaps part of the problem is that you are thinking about 'worth', and so judgmentally and dubiously, that people don't respond well. People pick up on those signals; they respond poorly to being judged. Or perhaps you are judging your own worth, which would be sad.
I find that my attitude and emotion greatly influences how the conversations go. Especially, give people space to flourish, be curious about them, and you will be amazed at what is inside - worlds of knowledge, insight and creativity that you never imagined. They are in you too, I'm sure.