Buses are not allowed to pick up or drop off at stops on the diversionary route. . When operators register a route they submit a map showing the route and the bus stops they intend to serve and this has to be adhered to.
This is not correct.
Buses are allowed to pick up and set down while they are on diversion.
Whether they do or not is down to the company running the route/local authority/TfL etc and generally decided on a case by case basis according to the circumstances of the diversion.
You don’t have to adjust the service registration with the Traffic Commissioner, unless the diversion is going to be over a certain amount of time (I think two weeks?) in which case you do need do need to re-register, but the cost is £0 instead of the usual charge.
With regards the point “There shouldn't be any passengers wishing to board/alight at these stops anyway as the service is not scheduled to go that way” this is often not the case - for example if buses have to serve the opposite side of a city centre than they usually do due to an event closing their normal route, then they will stop at alternative stops along the diversion route. I’m sure there’s unlimited examples of this but Leeds buses using Boar Lane instead of The Headrow is one that springs immediately to mind. If they didn’t stop along the diversion, no one would be able to get on or off in the city centre on the affected routes!
Similarly, a long diversion along a parallel road to the usual route will often see buses serve alternative stops, as this leaves a shorter walk to/from stops for affected passengers.
If a service is on an extremely long diversion, miles away from the normal route, that’s when you get into the territory of diverting non-stop as to do so wouldn’t benefit that route’s normal passengers and would exacerbate the delay from the diversion.