When my son was a toddler I had small family parties, so drops offs were not an issue. Or I had small parties with the neighbor children as "guests". Since I knew all the parents, and the kids often played together, I didn't worry about parents coming or staying. Occasionally a child from his pre-school would come, then the parent would stay - but it was a small pre-school class and we all knew each other so it required no extra effort.
Most parties that he attended were at places like Chucky Cheese so the parents stayed.
As he got older - 3rd/4th grade, if the party was at a venue, I would stay some of the time, but if it was at another child's house, and I knew the parent's I would drop off. I expected the same when we had parties.
I don't get the having to entertain the parent's also if the invitation is for the child only. I would not expect to have parents and siblings attend a party for my child...I simply could not afford to entertain 2 to 4 extra guests per invitee.
Anyhoo, now mine is almost 15 and parties consist of a few teen boys hanging out eating pizza and playing Nerf wars in the yard. Sooooo much easier. LOL