I have also been in this position a few times, where I missed the cutoff time for the first flight (or even the flight itself) and got rebooked for free on the second. Availability is definitely an issue, and I suspect timing also matters. Whereas I've never had trouble missing my flight by 30 minutes, I suspect if I showed up several hours late (as would presumably be the goal of someone wanting to take a later flight) they would not have been as accommodating. The former case is accommodated under what is typically known as the "flat tire rule" (although I think pmUS calls it something else) but this doesn't apply after like 2 hours from the flight. The stress of the whole thing makes it not worth doing by choice.