I just remembered something. There are songs in square dancers where the words are changed to call the dance. Years ago I was forced to take Folk Dance in college, and I remember a few lines from "Rose of San Antone."

Balance with your corner, she's the girl from way out west,
Balance with your partner, she's the girl you love the best.
tum ty tum ty tum tum, tum ty tum ty tum.
Balance with your Rose of San Antone.

I suppose if you sang these these words and played fiddle at the same time, it could be done. But it would be a lot of work to find and learn all those songs. And it wouldn't work for flute.
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I sometimes play for country dancing. There are at least seven musicians who come and go, and none of us attempt to play and call at the same time.

The brain is odd. I can play guitar and sing, but I simply cannot play the piano and sing.