I still guess that it wouldn't matter much for the gearshifting of the variator, but the heat that's lost in transmission of some 2 to 4 KiloWatts of power (depending on your setup) could be too much indeed with a smooth belt on the small diameter of the pulleys when fully geared up or down.
My old Vespa's probably never had more than 0.5..1 KW... although the front pulley was also very small... hmm, I've got a spare Agility and I'm getting curious now...