t'aint: yeah, same thing here - I did an hour's differences training followed by a checkride and we did enough hydraulics off to make you sure you want to check it each time !
Hovering is quite tricky at first: the time constant is much slower so you end up chasing until you get used to it. Still think that if I had a real hydraulics failure I'd prefer to run it on.
I always assumed such training was mandatory, but sounds as though it's school-dependent.
As for the light: well, if the hydraulics go off, you'll know about it anyway, so not sure what extra benefit there would be. A hydraulic pressure gauge would be more useful: might give some warning of an impending problem.