It doesn't help *if* the government is simply going house to house and demanding all firearms. But that is dangerous and incites rebellion.
On the other hand, if the government can tie a particular firearm by serial number to a particular person, they can say: turn in this particular firearm or we will stop your bank account.
If it is not illegal to own firearms where the serial number has been removed, they no longer have the power to tie a particular gun to a particular person.
And that’s the way I like it.