Himeaimichu

what's one example of such a band?

Wagakki Band in my opinion is actually a quite good example. Yuko is a really good singer, but in the recordings, her true talent often gets lost in the amounts of reverb and post processing. Personally, with her vocals, all I would do is use a suitable amount of compression and a suitable amount of reverb, but not as much as they use for this. In fact, Yuko has videos of her old stuff in Hanafugetsu, and some of it is just raw camera audio and she ironically sounded better on the camera audio.

If you're curious to how she sounds in some of the shot in one take videos of Hanafugetsu, here's a really good example. You can tell that she doesn't need nearly the amount of overproduction Avex gives her (I seriously have so many problems with Avex)

In fact, Hanafugetsu in general is recorded with not that much money, and it still sounds amazing. My rule is, if your vocalist is really good, less is more on the production. This studio recording of Hanafugetsu really drives my point