That's not how it was done where my children went to school.
Parents did not enter the building after an initial optional tour of the room that lasted about an hour the week before school started.
On the first day of school teachers greeted the children individually by name outside the school and sent each one into the building where the TA also greeted them and showed them where to put their bag and jacket.
My DD3 baulked and started crying inconsolably after being greeted by the teacher so I was allowed to carry her in and deliver her to the TA who took her by the hand and asked her to be her special helper for the day.
Parents stayed outside at pick up time too, and children were brought to the door and released one by one to parents/caregivers when they came to the door for the handoff. Children were expected to manage their own outerwear (taking off and putting on), and changing out of snowboots and into indoor footwear in winter, and the reverse at the end of the day. No parents ever entered to help children out of outerwear or escort them to their classrooms, or out again. Children were allowed to enter the school about ten minutes before classes started and they waited in class lines outside until then, with supervision provided by whatever teachers got outside duty on any given day. They entered the building in orderly lines. Parents could stay on the sidewalk and chat if they wished.
No parents who ever threw a party did so without having plenty of helping hands, in my observation and experience in the US. The vast majority of parties for children aged 4 to 7 were whole class parties too. Mostly the hosts had their own relatives or had teenagers lined up to wrangle the children.
The one party I went to where parents and children were all invited (in Ireland) featured children behaving far less well and displaying far less self sufficiency than they did at parties I threw with me and exH in charge and some teens hired to help out. The parents ether got in the way or just kept off to one side chatting and letting 'someone else' do the job of helping out. There is no need for parents to be frazzled. Plan well, make sure you have helpers who understand what is expected of them, and all will go smoothly.