Extensions and privileges in public schema

I'm teaching a university-level class using PostGIS. I have created a scratch schema for students to create objects in. At the end of the term I can drop scratch and start fresh the following term. 

Students of course can also create objects in public schema, and often do unintentionally because the forget to schema qualify their CREATE TABLE statements. This complicates things because I can't drop public schema without dropping various PostGIS (and other) tables and functions. Additionally, while I doubt the students would do something like drop a public function or supporting table (like spatial_ref_sys), it nonetheless seems like a poor idea for these database objects to be vulnerable.

What is considered best practices in this case? Should PostGIS extension be kept in its own schema (as was suggested when I asked about this on GIS.SE)? If I do so, can I treat public schema the way I have been using scratch schema, i.e. could I drop and recreate clean public schema at end of term? Should I leave extensions in public but limit rights of public role in that schema (so that they don't unintentionally create tables there, or accidentally delete other objects)? Or do Postgres DBA's just not worry about the objects in public schema, and rely upon applications and login roles to interact with the database intelligently?

To be clear, primary goal is to keep student created objects in one schema which can be dropped at the end of the term. But the question of preventing accidental creation/deletion of objects in public schema is possibly related, and the overall database organization might address both concerns.

Best,

--Lee