When we have ever done it (on very rare occasions), we have told the parent and child that someone has dropped out and usually we have booked an activity for say 6 or 8, so already paid for it (Laser Quest, WaterWorld, trampoline park, etc.)
Thing is, you have already paid the money. My daughter has wanted to invite more and we have said 'No, you can only have 6' or 'you can only have 8' because we can't afford any more.
Think you will find this is quite often the situation.
So, therefore, my daughter has wanted to invite the person you are now inviting.
Can't see any problem at all to be honest. Obviously not every case is like that, but I do think that it is often the case.