There is the little problem of “enforcement”.
1 - Many weapons have NO traceability.
2 - Many places don’t have “registration”, and would have to use ILLEGAL methods of tracing, via background check paperwork.
3 - Who is going to come and get the ones not turned in voluntarily?
“And how we burned in the camps later, thinking: What would things have been like if every Security operative, when he went out at night to make an arrest, had been uncertain whether he would return alive and had to say good-bye to his family? Or if, during periods of mass arrests, as for example in Leningrad, when they arrested a quarter of the entire city, people had not simply sat there in their lairs, paling with terror at every bang of the downstairs door and at every step on the staircase, but had understood they had nothing left to lose and had boldly set up in the downstairs hall an ambush of half a dozen people with axes, hammers, pokers, or whatever else was at hand?... The Organs would very quickly have suffered a shortage of officers and transport and, notwithstanding all of Stalin's thirst, the cursed machine would have ground to a halt! If...if...We didn't love freedom enough. And even more – we had no awareness of the real situation.... We purely and simply deserved everything that happened afterward.”
― Aleksandr I. Solzhenitsyn
4 - Many citizens will 'turn in' their guns and ammo, one cartridge at a time.