Surely the advocates are after federal level gun control laws rather than looking to make sure people have to abide by disparate state rules..?
Although it's illegal to "knowingly" sell against those rules, most buyers don't live by the "don't ask, don't tell" methodology. So in a lot of cases (don't have statistics on it), sellers will want to verify the buyer's home state, and probably even keep a receipt with the name incase the gun is used in a crime, and the ATF comes knocking at the buyer's door.
http://www.washingtontimes.com/news/2015/feb/11/federal-cour...
...the ATF comes knocking at the buyer's door.
Removing the seller removes supply and leaves demand in place, making illegal sales more profitable (and eliminating part of your competition); removing the buyer removes demand, making the supply less valuable (and possibly putting you out of business).
In the scenario of a transaction not documented in compliance with law, you wouldn't know where the buyer lives.