I think they should instead just introduce a clear system for verifying that a Raspberry Pi is genuine. For example, a code printed directly on the device. If you enter that code on the website, you can see exactly which model it belongs to and how often it has been used. That way, you could determine whether a Raspberry Pi is new or used and whether it has been modified.
I saw that once at a thermal paste manufacturer. They used it to solve the problem of counterfeit thermal paste.You just have to get people to actually use the system and tell anyone else who asks for support but doesn't have an original copy to GTFO.This would allow them to avoid the increased support burden without limiting people's ability to upgrade their Raspberry Pi.