Which tire? They have a couple UHP tires: the Versa & the Kaiser. What are the speed and load rating of the tires?
As long as you’re getting, or exceeding, the $/event expectations from the tires then I don’t see an issue with it. Safety would be my number one concern (tires and brakes are the top safety items). However, just keep checking the tires (this applies to any brand of tire) in between sessions looking for any strange issues with the tread (chunking, delamination, etc.) and/or sidewalls (bubbles, cracking, etc.) and if you slow down immediately on track at the first sign/sound of any sudden vibration/noise then you should be fine. I’d probably not run them down to the cords.
Number of days is going to vary widely. It’ll vary based on tire type, car setup with/without proper camber, staggered vs. square tire setups (i.e., how many tire rotations front-rear and/or side-side can you get), with/without aero, type of track (e.g., # and type of corners, # of left vs. right corners, uphill vs. downhill braking zones, etc.), proper vs. improper tire pressures, driving on them to/from the track, new vs. take off tires, car weight, etc. For 3-4 20 min sessions per day, three day event (excluding open lapping day for instructors/advanced group) starting with a brand new 200 TW tire that doesn’t heavily heat cycle out and are not driven on the street at full weight, I’d hope to get a min of ~6 events on demanding tracks, and a min of ~8 events on less demanding tracks. It’s possible to get fewer days, too
