The only sales which don't require bg checks are between 2 residents of the same state who aren't firearms dealers.
IOW sales between neighbors, friends, local classified ads, etc. There is no big money behind it. Manufacturers and dealers most likely would like the same restrictions on private sales as are on their sales, no? You can't name a single type of legal personal property which intrastate sale between private parties is regulated by the federal government. .none. Why? Because it is unambiguously prohibited by the commerce clause. States can restrict those sales, the feds can't.
This issue (the renamed "gun show loophole"

is the red herring. It has and does raise more money for gun control groups than any other issue. That is the money behind not making constitutional headway on the issue. .If the issue goes away so do a lot of donations to the big gun control groups.