What is the intuition. Higher quality turns due to more reasoning results in significantly fewer turns taken?

Yep. In particular, ARC-AGI-3 is a series of games where if you fail, you keep trying again (until eventually hitting a timeout). So the sooner you succeed, the sooner you stop spending tokens retrying. If it was a benchmark where everyone got one attempt with no retries, you wouldn't see it bend backward.

Yes, in theory.