Arranging a get-together at a restaurant where everyone pays their own way is normal in my circles. Everyone is just glad that someone else initiated a gathering. Usually though, if it's in honour of someone's birthday, it's not the birthday person who does the arranging.
One friend of mine got around this in what I thought was a good way. She wanted to do something on her birthday without actually saying, "Hey, it's my birthday!" So she simply organized a restaurant/pub dinner, the usual kind where everyone pays for themselves. She just didn't SAY it was her birthday. Halfway through though, someone looked at Facebook on their smartphone, saw that it was her birthday, and we all wished her a happy birthday. She never said that was the reason for the dinner, but I suspect it was. I thought it was classy of her not to make a big deal of it being her birthday.