I guess it's all about personal preference, and if good piano skills are high one someone's list, so be it. A word of warning about that though:
It's the job of a singing teacher to teach you singing. That ALWAYS comes first.
I picked up students from singing teachers who were great accompanists, but they hadn't taught them a morsel of technique. If asked what they did in lessons, singing songs/arias and working on them musically (which some people mix up with "technically") to full accompaniment always was the main focus.
One doesn't exclude the other, and a lot of singing teachers are reasonable pianists. It is a fact though that if you focus on an accompaniment, part of that focus is taken off the student, no matter how brilliantly you play. Every student who wants to learn technique has to be sure they are happy with that.
I play alright (wouldn't call myself a pianist though
), but the main focus of my piano lessons at Uni was to virtually simplify any arrangement - we've been specifically trained on this because they knew they don't teach budding pianists, but singers who only need the piano to study songs, or give the student a very basic idea about harmonies.
All the student needs is a basic harmonic concept, and even that doesn't come at the start. If they take exams, it is of course paramount they have practised with accompaniment, but that's easy enough to do (and not necessarily the singing teacher's job in any given case).
I had coaches myself who played the piano far better than me, and none (!) of them ever accompanied me during the technical stages, and only some would accompany when the song was a technical wrap. In fact, the higher up the food chain they were, the less they touched a piano (although they could have done a reasonable job). Probably because they knew their job is to pay 100% attention to what the student does vocally.
To the OP, I guess the question to ask is: What do you want/need? If making music is high on your list, you don't necessarily need a good technique teacher and are probably better off in a music ensemble of some sort (also cheaper). If you want to learn proper technique, you need someone who can teach it. And, as others already said:
Especially in singing, you need someone who can actually teach the style you want to sing, which is different from technique, but has implications on it (as in making certain choices to give you the sound needed for a certain style).
Crossover only makes sense if you want to be a crossover artist. In all other cases, it sounds comical