My car has an all included service package and they let you have new tyres at 2mm
Whether that's calculated or scientific or just a convenient round number to give customers some margin I'm not sure
My last few years of working we used leased company cars, our company paid for the servicing but the servicing had to comply with the manufacturers spec and the leasing company's spec.
This meant the car may not have another service for 12 months, so the question becomes will this item last/be legal in 12 months time? (the majority of our cars did go 12 months but 25% {High mileage} were serviced 4 - 6 months)
The garage used this to their advantage, they charged for all light bulbs, tyres, brake pads and disks, W/W blades, filters, injectors, belts, and some batteries.
Our management were unconcerned at this obvious fiddle so we (drivers) marked up a few components to see what had been changed.
Brake disks were changed but not pads unless very worn, filters were not changed, on the test car none of the belts were changed, nor light bulbs, 2 tyres out of 4 were changed, battery not changed.
So your 2mm tyre change would be to allow for another years wear.