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.
