My pov: working in a kindergarten in Finland.
It's really up to the parents but very few took advantage of the option to stay with their kids the whole time for weeks on end.
Anyhow, most of the time, however clingy and teary the kid is, they come around a few minutes after the parent left and start having a good time.
Parents need to be told this, encouraged to let go just like the kids.
And then it depends how the parents react when they pick their kid up: do they fuss, do they have a bad conscience, do they even ask the kid if it was sad, in other words, do they enforce and even reward the clinging, or do they encourage them to take their first steps into independence?
I'm not saying it isn't hard for kids, going to kindergarten for the first time. Social pressure, stress. But it's harder if parents are very protective and/or the kid had very little contact with other kids until then.
No idea what the situation is like where you live, but I'd go mad if I had 10 kids + 10 parents during the whole day for a whole week.
edit: hmm, this is also age dependent. I was working with kids 3 and up.