Is my thinking correct that Person and Site relationships should be modelled with the subtypes i.e. Desktop and Laptop rather than the supertype?
If I understand you correctly, yes.
The issue for computers, for example, is whether the real requirement is that one person has assigned zero or one computer. If that's the real requirement, then you should use the supertype. If not, you should use the subtypes.
One of the side effects of using the subtypes is that a person might be assigned both a laptop and a desktop.