Birthday party planning/inviting/paying

Apparently this is more “normal” in others eyes so I’m posting private to not be super judged… but I can’t help but think my mindset is more appropriate… So. Birthday parties AT an event place. If you are hosting a birthday party and inviting others to come, I thought it was standard that you pay for a bundle of kids to participate and celebrate your kid’s birthday. I’m talking about birthday parties at places like Chuck E Cheese, Skyzone, somewhere that it is necessary to pay per child. I’m planning my sons birthday party and yes money is extremely tight so I’m only allowing a certain number of kids to come (their fun pass, food, and drinks all paid by me) I’ve heard a number of friends/coworkers share some of their birthday party ideas and how they just let other parents know that they are invited but must pay for their own child. In my opinion, that’s not a birthday party then. That’s rude to expect someone to come celebrate your child and bring a gift AND still expect parents pay to for their own child to play at YOUR party?? Let me close with I am also in an extremely tight financial situation. I’m not judging anyone’s financial situation or lifestyle. The cost for my son’s birthday party is being split between 3 of us to make it happen. However, I wouldn’t invite other families asking them to pay for their own and bring a gift for my child… put a cap on how many kids you can afford to invite or stick with parties at the home, park, or public area. Event places for birthday parties should be accommodated by the host.