My hoster is doing exactly that. It automatically patches security vulnerabilities on all hostings for Wordpress, Joomla, Drupal and osCommerce.*

The feature is activated by default, you get informed when one of your instances automatically gets patched. It works very well.

Apparently they bought this patching solution from an outside vendor, wasn't able to find the name of the product though.

It's been quite the load of my mind...

* = Details in german, no affiliation: https://www.cyon.ch/support/a/wie-funktioniert-das-automatis...