I have a somewhat different take on this. I find Kavanaugh's statement respecting the denial of certiorari interesting. Not in the substance of what he said---that because AR15s are unquestionably in common use, the 4th Circuit's decision is probably wrong---as that was basically just summarizing what he said in his dissent in Heller II while he was on the DC Circuit. But the fact that he said anything at all in this context is interesting to me. He didn't have to say anything; he could have just voted to deny certiorari per normal. I view this as a long-shot attempt by him to persuade the Chief or Justice Barrett in the nearish term (i.e., the "next term or two"), while the Court is still 6-3 and Thomas is still on it.
There is not currently a circuit split between the circuits on whether "assault weapons" bans are constitutional (at least not to my knowledge). Any time we get a ray of hope in a panel decision, the courts reconsider en banc and uphold the laws. So, from a purely institutional perspective, there is less reason for SCOTUS to grant review. That, I think, is significant to the Chief Justice in particular, and also maybe to Barrett. I think both of those justices would be hesitant, purely from a temperament perspective, to buck a "universal" view of the courts of appeal if the Court granted cert. and heardthe case. So, I think that explains Kavanaugh's vote to deny certiorari.
Okay, but then why write about it? To signal to lower courts that now is the time to create the circuit split, if it can happen. Counting noses from this, you've probably got four votes to overturn outright AWB bans. If he voted not to hear the case but said nothing, folks would speculate he may have gotten squishy on it. By saying something, he reiterates that he hasn't. And by referencing the desire to have other courts weigh in, I think he's saying they need (or at least really want) a lower court appellate court opinion invalidating an AWB if they are going to persuade Roberts or Barrett. Thomas' repeated opinions and Kavanaugh's statement provide a permission structure of sorts for lower courts to go ahead and take that step, if there's anyone on the fence.
The issue is going to come to SCOTUS at some point; 2A jurisprudence cannot advance much until it does. I think Kavanaugh perceives the opportune window may be narrow but hope isn't lost. If Roberts and Barrett were for-sure no votes, I think one of the liberals would have joined the vote to grant certiorari to lock in their votes on the merits (or at least Kavanaugh would have voted to deny cert. and then not said anything about it). I agree that if Kavanaugh thought there were 5 votes for sure to invalidate AWBs, he likely would have voted in favor of granting certiorari. I think he's still trying to persuade Roberts or Barrett and is hoping for some help with that from a lower appellate court.
Barring an unexpected health issue for one of the justices, the compostion of the Court does not look likely to change during Trump's second term. Thomas and Alito are the oldest of the justices, so if there is going to be a change it's most likely one of them. Sotomayor and Roberts are next in terms of age, then the justices get relatively young. Looking at the odds of any future change in perssonnel, it does not appear likely to get better for the 2A any time soon. I think Kavanaugh wants to address the issue now because he doesn't expect the votes to get better in the future, but he doesn't know he has the votes now. So, he's sending out a call for help to hopefully nudge a lower appellate court to create the circuit split and provide Roberts and Barrett with cover/some assurance this isn't out of the legal "mainstream".
Whether any of this works, of course, remains to be determined. As soon as (or if) there is a circuit split and a court of appeals invalidates an AWB, I expect there will be four votes to grant cert. Then we'll find out if that's what we want.
Maybe I'm off base with all of this. I don't know the composition of the courts of appeals currently considering AWB challenges, and so maybe my thought of Kavanaugh sending up a signal for some judge on the fence is fanciful. Maybe the justices aren't this tactical with their cert. votes, or maybe circuit judges don't pay any attention to them when deciding cases. But this is what I was thinking when I read the vote breakdown and Kavanaugh's statement.