Look. I'm not an idiot. I write open source. I love free and open web.
Google login works. We use use Gmail - it works. We use google classroom - it just works. Most websites offer Google Login - it just works.
When you have 30 students and you waste 2 minutes logging into a website -- that is 2 x 30 == 60 minutes of student learning lost. Little things like that add up.
In yesteryears, no one could compute the things our phones do today in seconds.
But the demand for time has gone up, not down. Now idle time is a target to "get stuff done".
Even on HN, people have complained about how being idle during idle moments is a luxury, since everyone is on a treadmill to see how hard they can perform even in leisure.
The point being that when things just work, other long term issues being invisible, people will go for the cheaper option.
The same way people have burnt fossil fuels because the costs are sent off to the future, they will choose convenience over security.
But being observed by senior management, they would see students not learning. You could expect extremely close scrutiny for the next few lessons. To be put on special measures. Not quite a sack-able offence, but ....
I think your last paragraph would be sufficient to explain your reasons along with a single, "it just works."