I wouldn't be that worried if student accounts, especially for younger students, didn't have MFA. Teacher accounts should have it, and I don't think the problems you specify are real problems. I don't think there is any problem with a rule allowing teachers but not students to use mobile phones. Policies on photography would be independent of that, since they may have any number of other things they could use to take pictures. If phone use is that big a problem, issuing teachers with MFA tokens, either U2F tokens or a separate hardware device that generates TOTP codes is a viable option. Teacher accounts have too much access not to have that.
The separate issue of needing to authenticate too often is a good one, and that probably needs more thought to make it work. We would probably want different authentication policies depending on what's being accessed. Services with a login used for teaching without access to sensitive data could be on the low end, where a valid SSO token is sufficient to log into them, thus as long as the teacher has authenticated once today, they won't be asked to repeat it. Access to sensitive student data in the grading system could be on a higher tier where authentication is more frequently requested or usage patterns are used to determine whether to send that challenge. If students have shoulder-surfed passwords and used them to access or, as the article suggests, modify the data in there, this demonstrates that this kind of access control is justified.