Of all the things that you could've nitpicked, this is definitely not one of them.
-Everyone knew the girls were going to be punished because MC came in their class and dragged them to his office.
-Spanking was already established as a common punishment practice.
-It's not a secret that there are cameras around the Academy. It is a secret that they're broadcasting it live.
-If the girls knew that MC's Assistant was somehow watching him and the girls at the office, they wouldn't think too much of it. It was literally MC's first day and she was guiding him a bit so he knows how to do his job.
And finally, there are consequences that will happen if you choose some of the more perverted options, and will cause some of the students to realize something's going on.
I normally don't respond to criticism, I usually try to learn from them, but I just think this one is not an issue.