Oh, the old "we're not sure this will work, but we've got to try something" argument.
Sadly, in matters of public policy everything eventually comes down to a macro cost-benefit analysis. It sounds cold-hearted to put it in those terms, but when a public policy is being contemplated that has signficant costs, it needs to be evaluated in that way. So let's explore that.
There are likely at least 10 million rifles in the US that fit the broad definition of "assault style weapons". These are not cheap weapons. So a buy back would be incredibly expensive. At an average market value of $1,500 each, a buy back of them would cost $15 billion (assuming full compliance), before accounting for administration costs, enforcement costs, etc..
Then there is ammunition. If you are going to take the rifles out of circulation, the government would also want to take the ammunition out of circulation. And gun owners would certainly expect to be compensated for the ammunition they own for any rifle they would be selling back to the government. I have no idea how to even estimate the current stock of ammunition in circulation. But it has to be a lot. Let's say, for the sake of argument, that every rifle is accompanied by 200 rounds of ammunition (which I think is a bit low, but it's a start). The going price for 5.56mm rounds is $0.40-$0.50 per round. I would guess that 2/3 of the "assault weapons" in circulation are of that caliber. The AK-style rifles, which would likely be the next biggest category after AR-pattern rifles, fire less expensive ammo (either 7.62x39, or 5.45) that runs about $0.25 per round. Then there are a bunch of other calibers out there (6.8 SPC, .300 BLK, 7.62x51mm, etc.) that are more like $1/round. So just for round numbers, let's call it $0.50 per round, on average. That is another billion dollars.
So we have $16 billion plus admin and other costs, assuming full compliance.
There have been +/- 12,000 gun homicides in the US per year for the past several years. If "assault weapons" account for 2% of those, that is 240 per year. So, over the 20 years, one could expect a total of 4,800 homicides with that style of weapon, assuming no buy-back. A full compliance buy back would cost $16 bln in compensation alone, then figure +15% in admin costs and enforecement costs (which is likely low, we are talking about the government here) and you get to almost $18.5 bln.
That is a cost of nearly $3.9 million per life potentially saved over the next 20 years, assuming full compliance.
And that probably understates the cost/life saved, because there will be a substitution effect. Meaning at least some of those people being killed currently with "assault style weapons" would be shot with some other type of gun if the "assuault weapons" aren't available.
All of which begs the obvious question: what other types of public policy changes could save lives at a cost of almost $4 million per person?