I think even shot-for-shot remakes are fine when done right, which isn't very often. My most anticipated movie of this year is Eggers' Nosferatu remake

I think they're sad, creatively bankrupt exercises that generally shouldn't get made, but on the other hand, it's good when they at least do different things or bring real ideas to the table. Tons of horror movies really aren't very good, so you'd expect doing a good thing better to be a slam-dunk, but it's rare for a remake to actually take that and execute. Even a frame-by-frame remake has the potential to do better and bring out the best in a proven idea, or even fix something that wasn't appreciated from the many limitations a lot of old horror worked under. That's one aspect more specific to horror that makes remakes potentially a lot more useful to do, but it's still an issue that people making remakes happen are usually doing it because they don't have something better.

Friday the 13th (2009) did a great job mixing polish, old ideas, and tongue-in-cheek series self awareness that all make it a fun way to enjoy what was good as well as what was bad about the early F13 movies. Then you have things like Shutter, where the remake is basically the same but still manages to be worse at every opportunity on top of the weird and pathetic jingoism. That was just ugly all around, and pollutes the movie space, so now we have to be forever careful to clarify Shutter (2004) instead of Shutter (2008), because the only thing seeing the remake does is reduce the impact of seeing the better movie.

In my opinion, the only three (technically speaking) horror remakes that I can think of, which are actually very good are:

The Thing (1982) [forget the 2011 version]

Bram Stoker's Dracula (1992)

Mary Shelley's Frankenstein (1994)

In these three particular cases, the directors have successfully enriched the original stories by expanding on specific aspects barely hinted in the books or previous works. For example, the theme of sexuality in the vampyrism of Dracula or the true feelings of paranoia and isolation depicted in The Thing. All this with the addition of amazing visual effects, and great actors interpretations.