They work best for things that a human has to move, and since a good chunk of humans (at least in US/CA) have iPhones, the movement of the physical thing will be tracked by an iPhone fairly reliably. Any time the critter is outside the range of an i-device picking it up the location will be stale. There isn't really a way around that, since GPS/5G radios are a lot more power hungry than the occasional bluetooth pings an airtag broadcasts.

1. they way the network works, it works better for inanimate objects that don't move around

2. they contain small parts that pets might inadvertently eat, and some of the collars that exist for them have been known to snag on things and entrap pets.

I think mostly it's a chew risk for dogs and won't help if the dog is far from the AirTag network. I still have one on my dog anyway (he's not a chewer) and my daughter puts one on her cat occasionally. (Both pets are microchipped too, of course.)

I bought one for my cat, never did help with finding him, just the general area.

They're not great for tracking things that move on their own, or things that avoid people.