ELI5: How/why did humans evolve towards being optimised for cooked food so fast?

When one thinks about it from the starting position of a non-technological species, the switch to consuming cooked food seems rather counterintuitive. There doesn't seem to be a logical reason for a primate to suddenly decide to start consuming 'burned' food, let alone for this practice to become widely adopted enough to start causing evolutionary pressure.

The history of cooking seems to be relatively short on a geological scale, and the changes to the gastrointestinal system that made humans optimised for cooked and unoptimised for uncooked food somehow managed to overtake a slow-breeding, K-strategic species.

And I haven't heard of any other primate species currently undergoing the processes that would cause them to become cooking-adapted in a similar period of time.

So how did it happen to humans then?

Edit: If it's simply more optimal across the board, then why are there often warnings against feeding other animals cooked food? That seems to indicate it is optimal for humans but not for some others.