You are judging parents based on a snapshot of what you see of their life so yes YABU.
If you have to ask your kids 15 times to put on their shoes you can imagine that someone who have had to do the same followed by the same amount of request for the coat, scarf, to get in the car, get off of the car, to stop running in the aisle of the supermarket, might be at the end of their tether at the moment you might happen to hear them raise their voice at their kids.
So many things happen behind close doors that might lead to the outburst you notice and chose to judge.
I work in childcare and used to be a teacher, I have definitely raised my voice before, sometimes it's what it takes for the kid to focus and take you seriously and get things done. I can guarantee you that most teacher raise their voice, in fact at school, I found more bullying coming from teachers than I ever did anyone else.
Teachers will not blink at telling you aren't good for much, or that your work was ''pathetic'' I even had a teacher of mine tell us our lack of intelligence was the reason there was a rise in Nazism in Europe (I am in my 20's so school isn't that far off for me). Hearing ''you are an embarrassment'' from a teacher was pretty common for a student to hear growing up (and I have moved a lot so been exposed to lots of schools and teachers), some would even bring up personal things to embarrass students in front of the whole classroom.
So no, teachers don't ''sweet talk'' kids into staying calm, from my experience they can be appalling and use bullying tactics or use the '' you can go to the headmaster's office, or i'll call your parents, or you will get suspended, or you wont go to recess'' to submit kids into listening.
As a teacher I never ever bullied a student and never ever would have talked down to them but I would have had no qualms raising my voice slightly had it been necessary. As you said yourself, if as a mother it takes you 15 times to get them to put their shoes on, imagine the chaos if we had to wait for each kid to be ready and do things when they saw fit, nothing would get done, they wouldn't learn anything and they would continuously disrupt other kids.
Sometimes being stern is what's work best and if that's the case well I won't judge. I judge way more the parents who enters a 30 minutes negotiation of '' Come on honey'' with their kid who don't want to put their shoes on, making everybody late.