I do as well. #years in a row I've raised poults and chicks together. Sometimes I feed turkey starter and others I've fed game bird feed. Both high in protein and both worked very well.I frequently brood chicks and poults together. Whenever I do, I always feed turkey starter. I have never had any issues with the chicks being fed the higher % protein. At my supplier the chick starter is 23% protein. At the local chain store the chick starter is 18% and they charge as much for it as my supplier does for the higher quality chick starter.
It is my opinion that the suppliers push the lower % protein chick starters because they are cheaper to make and allow the manufacturer and the vendor to make a higher % profit and has nothing to do with what is best for the chick.