Lots of older guns, very high quality guns, do not have serial numbers and are perfectly legal.
So what is the difference?
I think the main purpose of the serial numbers is to tracks sales thru dealers. Older guns have already been sold.
Folks who remove serial numbers usually are not doing it because they are good people who were bored one afternoon. And if they were, there would be no way to catch them since there is no good reason for a cop to inspect your gun unless you have been involved in shooting someone.
Given that only 3 states allow ‘Constitutional Carry’, I think we have bigger fish to fry.