I agree... so why not host multiple dinners? On your own?
I started hosting my own dinners[1] at my house every Wednesday and it's been fantastic. Really super great. I can't advocate it enough, especially for someone introverted like myself who may not want to go out of his way to interact with new people every day.
The people that come to the dinners are people I meet through my roommates, or old friends, or workers at the local cafe (original and ongoing source of roommates too), or their friends. Sometimes we invite acquaintances on an off chance. Neighbors are fair game too. GrubWithUs would just be another "source" of potentially great people. After all if they don't click, you don't have to invite them next week.
Another similar event I started was a recurring beer tasting event with the owner of the cafe. This is a completely different crowd, fairly varied in age, but still small enough to be intimate and regular enough to make good acquaintances and bring people together.
There have got to be a lot of ways to introduce regularity into your life with acquaintances. Hell, even going to the same cafe regularly can help with that.
GrubWithUs may not be good for long term friends, but it does provide a sampling of people that you can in turn invite to your own regular dinners. It's a launch-pad for finding people to invite to your own regular events.
[1] Some photos: http://imgur.com/a/X2Zoj