I think your question could be clearer or more meaningful if you gave some examples that you think are typical.
But, even without example, the first thing I would point out is most piano music involves playing two part simultaneously. One of the reasons to slow down at the piano is to work out the rhythmic timing of the parts. Additionally you can run into fingering issues, like two awkward position changes at the same time, and slowing down allows you to work out those problems.
In both cases what you are really doing is taking the two parts and figuring out what the composite rhythm and action is. The composite, once coordinated, can then be treated more like a single action. At least working up the composite happens in the beginning. After a while, when the parts are well practiced, and your playing skills improve overall, you can start feeling the performance as two separate parts. Slowing down practice facilitates the process.
Singing one part doesn't involve that kind of composite learning. The only thing you're really coordinating with is the accompaniment or the beat. If the singer were also playing the accompaniment, like sitting at the piano and accompanying yourself while singing a song, I imagine you might slow down the tempo a lot to workout the issues of coordinating multiple parts.
There are probably some vocal techniques that require slow practice. I don't really know, I'm not a singer. But something like yodeling might need slow practice to focus on when the voice changes register. Vibrato would be another one. That isn't really the slow practice I think you mean, because it isn't about singing a tune slowly, but it would involve slowing down.