I see two ways this could happen:

They make it so you cannot run some models yourself without government approval, based on some criteria. For a random citizen, this would be harder than trying to stop piracy, and thus those willing to ignore the technical law may continue however they like, but it would be enough to block businesses from doing so. Kind of like how some software has a license that is a trap for businesses to have to pay if employees end up using it, but is widely popular among consumers that can get and use it freely. So the home market can do whatever if they really want, but the businesses and products those businesses launch can't ignore that sort of regulation so freely.

Another path is if they really get buy in that this is dangerous for mere peons to have: regulate hardware available for consumer purchase. Like no VRAM above 32GB, and nothing with the compute horsepower to go more than say 100 tok/s with a 32B model. Effectively setting a forever cap on home usage to current top-end 'consumer' and putting regulatory restrictions on beefier stuff. Consumer compute becomes just about improving power and cooling and form factor, no more expanding the capabilities beyond current top end.