I think you’d be run out of town here if you advertised gyros and didn’t serve it cut from the spit. 
Even the little ma-and-pop hamburger/hot-dog stands serve 'em on the cone. I’ve also wondered how it works with the food laws as, like your observation, I’m skeptical they finish a cone within four hours.
This thread prompted me to (a) have a lamb yeeros (which seems to be taking over from kebab as the most common term in my area) which as usual was excellent and (b) look up the relevant regs.
They seem to allow a more robust handling than some of the posters above would be comfortable with:
And a survey of shops
http://www.foodauthority.nsw.gov.au/_Documents/scienceandtechnical/kebab_poster.pdf
Yikes!