Yeah, auto reset.
I don't like them and I don't use them. If you pop a breaker it could be because something bad happened. If you're not an observant person you might not even realize something is cycling on/off every five minutes, then 2 hours later shit's on fire.
It's also nice to have the ability to open a breaker (turn a breaker off) for troubleshooting reasons, or to simply bypass something that is not needed or is causing problems. Good example is the automatic glow plug circuit on a diesel. It's nice to be able to turn off a breaker to save your battery from all the work of cycling the plugs maybe if you have a poor battery and a hot engine.
The " Are these meant to be sacrificial in the unlikely event they actually get tripped?" things are called fuses.