thanks to the whole reincarnation thing it’d presumably be difficult for the avatar to suddenly become evil since every previous avatar would screech at them and for all we know they could just force the avatar state to send the body to its death and exiting the avatar state just before death.

There's an ATLA comic that kind of refutes this, where Aang just straight up shuts out Roku. It's... not the best comic.

Anyway, I think the idea is that the Avatar is fundamentally the same soul reincarnating, the same empathetic petty thief that stood up for anyone that was oppressed. That's just part of their nature, sometimes to a fault. Even Avatars with a screwed up childhood like Kyoshi and Korra turn out that way.

The mitigation is often the plot, where their power isn't particularly useful to solve their problems. A poignant example is when Korra just turns herself into Zaheer to save the Air Nomads, fully expecting to die (though the gravity is not very explicit since it's a kids show, as is true across both TV shows).

, and ONE person is effectively just a god,

Another thing I find amusing is that "common" people just treat the Avatar as some random joe, with lines like "Avatar, huh? We still have one of those?" or Bolin's grandma who clearly holds more reverence for the Earth Queen than the Avatar.

As far as fantasy series go, I think it does a good job of making all the Beautiful Special People feel mundane.