So recently, our D&D party defeated a (slightly homebrewed) ancient black dragon and I think I finally understand the appeal of high level combat in D&D.
The fight stretched over 3 sessions, we needed an absurd amount of healing to stay alive and the first two sessions it looked like a really close call. But by the end of the third session, everyone could pull about 2/3 of all available stops and the dragon was feebleminded and effectively stun locked.

Probably the best D&D fight I have been part of. You can't really get that feeling of accomplishment at low levels where few battles last longer than a few rounds. But I could easily see it going the other way with a less competent DM since it's really hard to balance fights on such a scale.