My first thoughts are very similar to yours; the Fed does very little well, except the military.
The second thought is, if this becomes law it will now be a national privilege, no longer a right. If it HAS to pass, my request would be to bring it under the 2A; therefore, making it a right. After it passes, this opens the door for this law to be tweaked, depending on the party in power, to their wishes; possibly requiring national training and a host of other hurdles to climb, in addition to the individual states requirement.
I know on the surface, many think it is harmless, in fact, a win for the 2A. This is the fallacy. It will not be like this in the future; if Dems regain power, then they will adjust to fit their anti-agenda; the Repubs then adjust it to fit their agenda. So, year to year it can become a ping-pong ball. I know the NRA says they will police this bill, to make sure nothing happens to it. Although I am a NRA supporter, I don't want this to be policed by them....again opening the door for even more political fondling!
As to it passing; I'm getting the funny suspicion that KO would sign it; it is an election year and it potentially could garner him votes...he'll sign it. He would love to say he is 2A friendly. As of right now, he hasn't been anti 2A; his administration has made comments that they are, but his actions speak differently.
That's my thoughts in a nutshell.