What other single purchase game in the industry has continued to develop free post-release content for five years?

I'm explicitly referring to content that isn't free. Abandoning a game doesn't mean you stop making free things, it means you stop making things in general, paid or unpaid.

Why does it seem like Diablo is the only game beholden to this standard?

It's not. The game, like many others in its genre, is designed for replayability. Replayability isn't dictated by how much new content you can generate.

D3 has a handful of sets for each class - once you've tried them all, you've experienced about 95% of the game, and a set can take a mere few days to collect. The challenge is then to find better rolled versions of the same gear, and to do a dungeon where numbers are tuned higher the further you go. That's incredibly fun for a month or so but that's it. D3's idea of replayability was constantly churning out new sets of armor... this is not sustainable. The Necromancer class, while a cool throwback, will likely not be worth the $20 and it doesn't really provide any additional content besides the character (and subsequent items) itself, and maybe a quest.

As for what made D2 special, it's hard to explain if you haven't obsessed over it, and I was never super into it but I did spend a lot more time on it than with D3. I think the thing people loved about D2 was remaking characters for certain builds, PvE or PvP. It was restrictive in that you could easily allocate stats incorrectly, but if you were into min/maxing, trying new builds, new items, it was fun. It sounds counter-intuitive, but a lot of the fun of D2 came from how busted and difficult it was... though PoE has managed to show that you can still have the same fun in a modern game. (Personally I'm not a fan of PoE though)