I wanted the license file to be associated with the user's personal information (name and email) so that there's an incentive to keep it private and not share it on forum, etc. (I think that's how Total Commander does it as well, as I see my name and post code/town in the About box).

The public/private key allows doing this by signing the user's information. A serial number is more anonymous as it doesn't carry in plain text any information.