I have seen dozens, probably hundreds, of queens return to apideas and I have only seen a queen showing the mating sign twice. I saw one enter an apidea and by the time I had the top off to get a pic they had it cleaned it off her and that was less than 5 minutes from I saw it.

Where you are almost guaranteed to see this behaviour is the first sunny afternoon after a couple of weeks of poor weather.
Beo Cooper argued that AVM was a strategy for mating locally in poor weather but that is definitely not what I see.
This happens when it is sunny, calm and usually 18c or more.
Most of my sites have 50 of so Apideas so if the conditions are right several should take a mating flight on a good afternoon.

Phil, if you witnessed this you would see that there is definitely something very coordinated going on on the part of the bees.

I must go and check that one I mentioned in the OP as she should be laying this evening or tomorrow.

I can see how there is a doubt as to whether she actually mates within this swarm from the apidea but I do not think there is much doubt that this behaviour has some role in the mating process, possibly the central one.

Leaving aside any interpretation re mating, why would bees and a queen leave the security of a hive/apidea, fly round in a tight circle for 10-15 minutes, cluster in a ball for an hour then return. It's hardly for their own entertainment so it must have a purpose.