I think the scenario you have described is very different to the one the OP is envisaging from what has been said.
Some people expect 'the kids' to he kept out of the way so that adult conversation/fun isn't interrupted.
For teenagers who are expected to do that, it's not a welcomed social opportunity or a bit awkward until you've got to know people, it's an evening of being expected to entertain other people's children, keep them quiet and out of the way so the adults don't have to deal with them. Any boredom, poor behaviour, accidental breakages or spillages become something the teens are held responsible and told off for because they're older and the ones in charge and someone had to be responsible and the parents don't want to tell someone else's child off or cause a scene by addressing the parents, so the teens get it. And the guests aren't managing their children properly because they're a bit tipsy, and it's the babysitters job. Only the babysitters weren't asked, didn't agree to it and certainly aren't getting paid for it.
Don't pretend that it's the same as going to a party as an adult where you don't know anyone but can drift around the room making small talk with whoever you like until you find someone you want to chat with.
And, whilst I appreciate that there are lots of different experiences and Los of diffeent families, the crucial thing is that, in this case, the OP's children have said they don't want to be put in that position so they must have a reason to assume they might have experienced this before and I think, at their ages, it's reasonable to take their needs into account too.