I find there are two general crowds when it comes to hunters:
-The first has the philosophy of "dead is dead" and don't really care about lost meat, good shots, suitable cartridge for the job, and sometimes even whether it's a humane kill or not. If they get to put something in their freezer, nothing else matters.
-The second prefer good, clean shots, minimal lost meat, using the proper bullet and suitable cartridge for the job, and a quick death for the animal. These are the kind of people who would rather go home empty handed than make a bad shot and cause an animal to suffer unduly.
As en extreme example I once ran into a group of 4 older men who where looking for larger capacity mags for their Lee Enfields. They said it's just a fact that sometimes you need more than 40 rounds to kill a deer if it's running. I believe they where hunting with FMJ surplus from decades ago to boot. I just pictured 4 men kneeling in a line blasting away at a running animal as fast as they could. Made me shake my head and walk away.
I saw pictures from a white tail killed with a Hornady A-MAX which is essentially a BTHP with a polymer tip. It's a target bullet where the lead is not bonded to the copper jacket so separates and causes a lot of collateral damage. The entry hole was as expected but you could almost fit a basketball into the exit wound. The kill was made with a .300WSM from under 50yds (so hugely overkill even with the right bullet). The bullet just disintegrated and almost cut the deer in half. A BTHP in a .308 wouldn't do quite the same damage due to less energy but the results would be similar but on a smaller scale.
I've also heard of cases where a BTHP has its tip bend over when it hits and punches through like a FMJ causing almost no damage. Simply put they are accurate but not reliable in how they respond to impacts.
A non-bonded target bullet (like a BTHP) will kill a deer; no question about that. But for reliable response on impact and reduced damage to the animal I would always go with a hunting-designed bullet if I can (which today is pretty much always).