Unless you've got a surplus of highly-perishable food, a surplus which will end as surely as winter follows after fall.

Plausible. How often do people eat most or all of their tame animals in late autumn, and adopt new animal babies in spring, instead of maintaining bigger herds of tame animals that can reproduce to replace the ones eaten? I remember hearing about something of the kind, but can't recall the details...

The question is, then: how viable is taming and raising animals for short periods of time before eating them?

Even if there's overlap between human and potential-pet diets, that doesn't mean they're in direct competition. Dogs, for example, will happily eat the same fresh meat a human would, but can also survive on gristle and partially spoiled meat that human stomachs violently reject.

Spoiled meat isn't something you have a reliable supply of. You can't raise a dog just on spoiled meat and other things humans won't eat.