1) if people reported the gun stolen you achieve all of the above
I already addressed this.
IF every person reported a gun stolen, then yes there would be no objective benefit.
However, every person doesn't report a gun stolen. And not just for nefarious reasons. Negligence, laziness, ignorance of the requirement could all contributed to a reason why someone would not report a gun stolen.
In the event that a gun was stolen or lost and then was used in a crime, but the person didn't report it stolen, then registration would potentially allow LEO's to more easily learn this fact and possibly gain information that could help with the investigation into the current crime at hand.
2) the police already have the tools to find who was the retail purchaser of the gun
Already addressed as well. Registration would provide a much more expedited method of determining who the last legal owner of the gun was. Determining that faster, and with less resources, is objectively a benefit.
3) do you think someone who leaves a gun they know is registered to them at the scene of the crime is realistic?
I believe it's absolutely realistic to occur in certain cases. Routinely? No. But criminals, and people in general, are hardly renowned for always thinking logically or with great forethought. People, in general, sometimes do poor decisions in crisis situations.
Even if it happens rarely there is some objective benefit from it. Unless you're suggesting that 100% never happens?
Again, as I said in a later post....if the question is "Is there any objective benefit of gun registration that is substantial?" then you get a different answer. If the question is "Is there any objective benefit of gun registration that overrides the potential negatives?" then you get a different answer. If the question is "Even if there are benefits, should we do gun registration?" you'd get a different answer.
But the questoin seems to simply be "Is there any objective benefit of gun registration".
Looking at it objectively, and without a preconcieved bias one way or another or an irrational fear of "OMG! If I say something that isn't 100% lock step in line with the most extreme of pro-gun people then I must be anti-gun!", I can honestly say that yes....I can see some objective benefits to gun registration.