On Arch Linux, the browser would often crash after the system upgrade installed a newer version of Firefox. I read on their bug tracker that the upgrade prompt was a workaround for this (or at least one reason for it).
Similar to how pacman (by default) removes all modules for the current running kernel, during an upgrade?
..which then breaks pretty much everything that relies on dynamic module loading, such as USB.
It's similar to how, when you install a kernel update, new devices are not recognized anymore because the loadable kernel modules on disk are for the new kernel version, but you're still running the old kernel version. (There is the workaround employed e.g. by Debian where old kernel modules are left on the disk until they're cleaned up manually, but that opens the "manual cleanup" can of worms.)
I think it should be possible under Linux. Firefox could pass the old libraries as file descriptors to its child process and and the child could dlopen those through /proc/self/fd/... . Or a more robust mechanism along these lines. But I wouldn't seriously suggest that Firefox should do something like this, restarting Firefox every once in a while is fine.