Firing people who accidentally install malware seems like a tremendous waste of what a human has to offer a company. Can you really afford to lose someone over something like that?

If there is a pattern, yes. Nothing I do comes remotely close to accidentally installing malware. If they install malware it is probably because they are using their work-owned computer as their personal computer. If they are doing that they are doing something not very smart and they are probably making many other workplace mistakes.

On the contrary, I work at BigCorp where every machine is locked down - no administrator access, no sudo, etc. People routinely install programs to C:\ simply because it is writable. If you need admin access to install it? Forget it, open an IT ticket.

I've never heard of anyone quitting because of this issue.

Yes. BigCorp have very limited access to resources depending on their role. IF you need to install software OR require admin rights your ticket have to pass long tail of approvals with lots of justification.