You can provide a repo hosting your software so that prospective users can add your repo. This is essentially trivial and can even be hosted for free.
After your user adds your repo updates will be handled automatically with the rest of the system and installs can be done in the same software management gui as anything else.
Schools almost exclusively use Microsoft Windows. Linux is almost exclusively used on servers, technical peoples workstations/laptops at work, and interested users personal computers.
Optimizing for users you wish you had doesn't seem optimal.
In the hypothetical school setting you probably want to actively prevent the user installing insecure crap in their home directory to the degree its possible to do so.
After your user adds your repo updates will be handled automatically with the rest of the system and installs can be done in the same software management gui as anything else.