Because this DOES happen.
Add this one to the rental car checklist before driving off the lot. It is also one of those seemingly overly cautious things, until there's a pretty Ford Fiesta with the prettiest flat tire staring right back at you in the face.
The longer story is that rental car agencies are not legally required to carry a spare tire in the vehicles they let to renters.
TripAdvisor user TravellaLott points this out:
It [is] because car models do not come with spares. Instead, they have emergency tire inflation kits. Improves gas mileage supposedly by not having to haul around another tire.
In a worst case scenario, spare tires are being increasingly replaced with a can of sealant—used to seal the hole on the tire so the car can be driven to a safe spot—but don't count that as a guarantee either.
Our tire was so blown it wouldn't have mattered.
As to for who is on the hook for the cost of towing the car and replacing the tire, that depends on the agency and what the car insurance situation looks like.
(Enterprise did not charge us, since it was included in the rental. However, we did lose three or four hours on the road fixing the problem. A much smarter, and time-efficient, solution is driving to nearest agency lot and swapping out the car.)
Great American road trip, anyone?