If the private key is on your computer, that's not very secure. I wouldn't trust myself to fully secure my computer, let alone the average person.
The part I liked about the system in Slovenia isn't so much the particulars of where or how the certificate is stored, but about how it's issued. Since the bit I was answering was "But how do you map a key to a person"
Perhaps a better approach regardless of how it's stored is notification of use?