Er… actually the main argument does apply - the one virtually every non-US country has applied (and even the use half-arsedly applied in the 1990s) - ban large-clip weapons, ban military-style weapons, make possession of them a federal crime, and force all states to comply with some federal gun laws, rather than making up whatever laws they feel like.
You could also start by criminalizing all methods of causing a semi-auto to fire like a fully-auto.
This is mostly true but you’re misunderstanding his point.
His point is that gun laws do not need to be ultra-specific to work. They don’t. They really do not. You could get that to work in the US.
The problem you point out actually has nothing to do with litigiosity (is that a word?), and everything to do with how jurists (judges and lawyers) operate in the US as compared to the UK. You are correct that technicalities tend to rule the day in the US. In the UK, justice rules. I don’t mean that in some ponce-y way, but that’s the key difference. In the UK, technicalities do matter, but justice has to be done, and some technicalities can be overriden in order to it. We give strong weight to the intention of the laws in question, not just the precise wording. I could go on about this all day - there’s tons of legal theory (there are actually at least four fundamentally different approaches to this issue), but US jurists tend to put the technical wording as the number one factor, and often let justice DIAF because of that (this has been particularly bad with some forms of sex offender in the US getting off continually on technicalities despite being arrested quite frequently, because obviously they’re committing a moral crime - peepers and upskirt photographers principally).
HOWEVER, you can word things broadly. The problem with a lot of current US gun laws is that they are overly technical, and this CREATES a multitude of loopholes and potential interpretations. Simpler, more straightforward laws, which don’t attempt to hyper-classify things could do a better job AND reduce lawsuits and vulnerability to lawsuits. However there is no political will on the right to improve the situation. Absolutely none.
There may be in future. The NRA, the main lobbyist group pushing money into politician’s pockets on this, is currently imploding due to have drunk the poison of the alt-right. The NRA used to play it smart and defend gun-owners generally, and gun ownership generally - particularly including black people (who own legal guns at at slightly higher rate than white people). That ended a couple of years ago, with some leadership/strategy changes. They decided to go full on racist nutjob alt-right, and now have a TV channel called NRATV which features every nutty alt-right perspective you could hope for, and instead of defending black people owning guns, they’ve just gone the “be afraid of all those blacks!” route, race-baiting and so on (they do have one black presenter, but he’s a long story!), and just putting out all sorts of conspiracy-theory-ish stuff that the NRA of, say, 2000, would have screamed in horror to see.
So yeah that may change. Not because of an incident like this, but because the NRA may make itself entirely politically toxic.
(As an example of how needless over-precision has made a mockery of US gun laws, you might look at this: https://www.youtube.com/watch?v=WP5KbWOe64g - a gun manufacturer has created what is obviously a short-barreled pump-action shotgun with a stock, which is kind of illegal or at least subject to heavy regulation, but by skipping precisely on poorly-worded and largely needless over-precision in the laws - actually regulations I think in this case, but deriving from laws - to create what is merely a “firearm” they thus avoid most of that. Or have so far. I mean it’s so sketchy the dude can’t even shoulder-fire it but… Despite, again, the fact that it is very obviously a short-barreled pump-action shotgun with a stock. At least it looks like a total piece of shit to shoot! Ugh that action. I’ve fired SA-80s and that still looks painful to me.)