One, gun control advocates would never accept it as they really want registration and it would put the lie to their meme that they just want universal background checks.
Two, it would be a counter proposal that the media would have to report and would take the wind out of the universal background check meme, see above, and would put the gun controllers on the defensive.
Three, if it did pass, allowing one gun or multiple guns to be transferred with an approved transaction that only notes the seller and the approval of a buyer with no record of the gun or guns involved being transmitted there would be no way to track individual guns or groups of guns. Even if they cheated and kept the information it would only tell them the name of someone who bought/received a gun without telling them what they owned. So theoretically an individual could buy five guns one of which was an old shotgun, turn around and sell the shotgun in an approved transaction and keep the rest and the government would have no way of knowing what if any gun that person had. Basically all the paper trails from FFL's on guns could be wiped out with one transaction, especially if the legislation superseded state laws like CA where now all transactions are required through an FFL or even states like IL where records of individual sales are supposed to be kept.