Other than personal comfort, this is a perfect example of people inventing stuff to worry about ...
If a (liquid cooled) bike would overheat from simply sitting at idle at a red light or if the battery would drain fast enough to cause a problem (from the fan running), that would be a MAJOR engineering failure for one or the largest and most well respected motorcycle manufacturers.
I have never heard of an FJR overheating at extended idle nor have I ever heard of a battery draining (to a detrimental level) unless there was some underlying problem prior.
If your bike is maintained well and running as designed, I guarantee that it can handle it ... They test and certify these things at extreme temps ...
Now, as far as the Phoenix guys are concerned, shutting it down to avoid boiling your legs over makes a lot of sense ... I visited there once and it is uncomfortable in the shade (let alone on a hot FJR) ...
We've had this discussion before. People who don't think there is any possible harm by letting the FJR idle with the fan running for an extended period are welcome to do so. Engineering is done within a set of constraints, in particular cost and schedules, and not everything is designed to satisfy the maximum possible conditions. A design point may very well be that the electrical system be able to maintain the charge at idle in 100+ degree heat forever, but it will more likely be that it can do so for some reasonable amount of time which will satisfy most conditions. Didn't the fallible Yamaha engineers design a ground wiring harness that could not satisfy all conditions? And an ignition switch with a similar problem? And something about an ECU which did not sample ambient conditions often enough to deal with changes in altitude?
I remember someone posting that they did indeed have the battery go dead from waiting in the customs queue entering Michigan from Canada, but I don't remember the details so there may be more to it than just the fan running at idle.
I certainly agree that shutting it down to avoid the heat building up for the rider's comfort is a good idea. Once all that aluminum and fuel and steel gets hot it takes a long time for it to cool back down.