I got a vette with bald tires once (yes...BEFORE I rented it )

I debated it and figured, well..it's not raining, so I'll go for it. I told them about it after the rental, and can only hope they fixed it.

Under hard acceleration, it was a little squirrelly even on dry roads. I think that tires should definitely one of things they check, but as you found out like me...they aren't. So, I guess it's up to us to take a quick look before leaving the lot.