I don't agree with the 'yuk' either. And the thing about random is you can't make a pronouncement until you are finished. I sort for value if necessary: light, medium, dark and put them in paper bags or plastic grocery bags. Reach in a grab. I don't have a problem with 'random', the bags just keep them from travelling all over the place.
I think I'd try a small project. If you truly hate it when you're finished, then random is just not for you.
A word of caution: a friend of mine from guild did a quilt last year. Supposed to be random but she just couldn't stand not controlling things so it's scrappy but very controlled. It's a nice quilt, but she's disappointed that it doesn't sing the way the one in the pattern did.
And the only way to get those amazing surprises is to be random....
Have fun!