Has this ever even been confirmed, though? Because the impression that I got from the recent NYTimes documentary about Jan. 6th was that the "waving" wasn't to wave insurrectionists in through the gates as opposed to a tactic to manage the USCP's retreat & pull-back as efficiently as possible following the overpowering rioters' break-through of the barricades, in that the officers manning the already broken-through barricades were being urged to not remain behind amid the crowd.
No IIRC. It's a meme from the Morning Joe crowd.