I had an interesting conversation with my husband a few days ago. We are throwing a 6th BD party for our twin girls at The Little Gym. (We had accumulated enough points on a rewards card to get the party free:-)) He asked me if we were paying for all the children.* With big eyes I replied, "Of course!!! You don't invite people to a party and ask them to pay!!!" I was horrified. He looked taken back and said with indigence, "Well, I don't know!" *he doesn't also retain information I give him like "we are getting this party for free:-))"
My husband is the sweetest, kindest, gentlest guy ever and when people are over to our house he is the most gracious host. When we go out with friends or family, he often wants us to pick up the tab, especially with friends or family members that we know have less than we do. But, he's never thrown a kid's BD party at a location where we had to pay. And I guess he had assumed that I was paying for the girls when we went to other parties. He simply didn't know. There was no malice or cheapness intended when he asked me the question; he just didn't know any better.
So, I'm hoping that parents who do throw parties and ask their guests to pay just don't know any better. Maybe this is the party their kid really, really wants and they just don't want to say no.
That said, I probably wouldn't go to a party where I had to pay for my girls to go. Especially one that would cost around $45 once you factor in a gift. I would consider letting my girls go to say, a day at Kings Dominion, with a very best friend. But it would be a special circumstance.
When it comes to adult parties, I would be less a stickler about a group getting together for dinner to celebrate the birthday person. In that situation, I would assume I was paying for my own dinner and would be happy to chip in for the BD person's dinner. If it wasn't a place I could afford to go, then I would decline. I have fewer issues with this because I think it's fine for adults to want to get together with their friends on their BD and unreasonable to expect most people to be able to pay for everyone's dinner - even at a cheap place.
*edited to add - *I wouldn't condone parents throwing parties and asking people to pay, I'm just hoping that in most cases it's ignorance at play instead of cheapness or rudeness.