It's probably relying on normal process isolation (and extensions run in a different process), but in order to disable stack dumps for it, you'd have to have some way of indicating "this process is special", which rules out treating it like any other extension.

Maybe there could be some new extension permission for "encryption extension" or something, but it's possible that could be abused...

There's already permissions that are only usable by Google's own extensions, so they could do something like that.