I would suggest drop tanks use is outside the scope of the American definition of recreational diving
No. It's inside the scope.
On dive #3 of the Deep diver course:- "The Student divers perform an 8-minute simulated emergency decompression
stop while breathing from an emergency air source for at least one minute."
The need for the 8 min emergency deco stop is a carry over from tables.
That said, often for some students it's a tricky little skill, requiring them to maintain buoyancy while task loaded at a stop.
A high proportion of dive centres especially where their main customers are vacation divers, place a drop tank near teh line on deeper sites.
Thus its a requirement to teach DM's how to rig one. On my DM course the frequently used cylinder is of course pre rigged in a stage sling, so one exercise simulates that cylinder being out of service and them having to cobble together a rigging kit from stuff on the boat. This exercise while simulating a likely real life event, also teaches and reinforces their abilities to problem solve and safely carry carry out non routine tasks.
So while the points you make are fair, the requirement for DM's to have the knowledge and experience to rig a drop tank are certainly within the scope of recreational diving.