Linux has Gnome-keyring, which, amongst other interfaces, operates as a PKCS#11 softhsm (I think), but it still runs as your user.
That doesn't mean that the solution is worthless. It simply means that it doesn't cover an unrelated class of bugs.
Migrated to hardware-based tokens, or Intel SGX-protected software tokens, would extend the solution to cover the case of arbitrary code execution. That doesn't eliminate the value of the software-only solution.
You need root to get at the keys otherwise. There is code to do it here: https://github.com/juuso/keychaindump
(This pulls the key wrapping key out of the process and then decrypts the keychain file directly.)