Even if our kids go to a party at a centre where activities are organised ie. soccer, gymnastics, trampoline, ten pin, etc. one of us will still stay as it's also a great social time to connect with other parents and there is a wonderful sense of belonging and community amongst the parents at DS's school. Not only that, but it means that the hosts can also relax a little more if we're all keeping an eye out for our kids, taking them to the bathroom, helping serve food, clean up, etc.
I think everyone knows that hosting has a bit of pressure to it so are quite happy to help out or at least keep track of our own kids. We had guests come (relatives) to our son's last party whose behaviour was appauling and dangerous and I had to reprimand them and keep tabs on them whilst also helping my middle children do the activities at 38 weeks pregnant. Their parent was MIA.