Is there a crypto“currency” that doesn't enrich its issuer?

Interesting question, as I think every single project out there benefits from increased adoption. And, if you "own" something that means it has some kind of value attached to it. I don't think you can escape from that.

But anyways, I think a project called GridCoin is an example of a cryptocurrency being used for altruistic ends. It is based around volunteer computing and you are awarded GridCoins as credit for doing charity computing on BOINC. Instead of brute force hashing, your PC does work on things like climate prediction models and protein folding. That being said, these coins are something you can trade away once they have been awarded. They are "worth" around 2¢ at the time of this post. There is certainly an incentive to get more people on board, and you would gain from the value of these coins going up. But at the same time, these projects would get more computing power. So make of that what you will.

There have been a few of these over the years (e.g. Taler, Reserve) but they always fade away because they don't have any funding and the use cases aren't as compelling as people think.

Yes. It's called Bitcoin.