We have one bath without a back splash behind the vanity. The vanity has a single-piece sink/counter top in white porcelain and there was no way to install a back splash without it looking very jury-rigged/after-market. It is an extra/guest bathroom and doesn't get a lot of traffic, so I decided to skip the back splash.

For a heavy-use bathroom I would never have done that.

We redid our bathroom about six months ago and our contractor told us that a backsplash was not necessary. Water proof dry wall (whatever the kind is that is specially designed for bathrooms) was used, plus we used paint designed for bathrooms (ie, also waterproof). Not sure what kind of dry wall is in your bathroom, but if it's new, it's probably this treated version. so far, no evidence of problems on our wall, and it's in our highest-traffic bathroom.

In the thread linked above, the homeowner planned to tile the wall.

I think tiling the wall looks best, but if that's out of the question, I could see using the piece that matches the counter to provide a little protection. I don't think that's necessary, though, unless the bathroom might be used by kids.

Someone else recently posted this question. I don't know that this will help, but here you go:

https://www.dcurbanmom.com/jforum/posts/list/702366.page#12379524

It doesn’t take much water to damage drywall. I’d put some kind of backsplash, or tile the wall.

Our bathroom vanity abuts drywall, not tile. I'm deciding between installing a 4" marble backsplash against the wall behind the vanity vs. just having the vanity flush with the wall (without a backsplash). I like the latter look better, but I wonder if the backsplash is necessary to protect the wall from moisture from the sink. Thoughts?