As much as dining alone can be bothersome to me, I think the idea of dining with a stranger and then adding that stress on top of everything would be more than I could take.
I tend not to choose fancy restaurants, but instead stick to fast casual places, diners, etc. I also try to go early or late. Often times you can strike up conversations with the wait staff. I find it easier to dine alone in smaller, quieter places as well, ethnic restaurants seem to be good at this.
I also find it easier to eat in a business district - there it seems more "acceptable" that you are dining alone.