The system does not break because the bloatware is missing, but because to remove Edge you removed the privileges of the system account used for system updates. The method described is what breaks Windows, not the removal of Edge. There are exploits allowing an administrator account to impersonate TrustedInstaller: it’s possible to uninstall edge without breaking Windows Update.

I think you’re too much optimistic about the impact on education: Every kid will have an AI in their phone, and instead of thinking by themselves when they’ll have a question they will just ask the AI and forget the answer quickly because they just have to ask again. However I would be happy to be wrong.