Isn't that how the world works?
Not for everyone, no. It really is not that simple for many, many people.
OP, whilst I can see that in your head this sounds a great compromise and wouldn't upset anyone, unfortunately (said with kindness as tone gets lost online) I think you may be getting slightly lost in Wedding World, which is somewhat apart from Real World.
You really, really should not put this in an invitation. You will look a cheeky mare even to those without children and therefore totally unaffected. And weddings have a way of causing long term changes in relationships with people somehow, more than a one off row would do.
Invite close family and their children, plus close friends and their children IF you know them. Not your friend from work with all their family that you know exist in the abstract but realistically are not part of your life. For them, just invite friends plus partner.
If even that leaves loads of kids to pay for, invite just the adults on the more emotionally distant invitations. (Not sure how else to phrase that!) Don't say "child free." Leave that open to interpretation. The assumption for most would be adult only. And then if anyone queries that, you have an opening to explain your dilemma and share your idea with those it could affect, who are the only ones who need to know it is an option. Just be tactful!
And really, it comes down to your particular group of family and friends as to how they would receive that idea...which is something noone online can help you with.
Congratulations on your wedding, hope it all goes well no matter what you decide to do and that you have a wonderful day!