GH,
“I would agree with you entirely that logically, there is no logical nexus between a yid being married and having the requisite attributes for being a chazzan”
Yes there is a sense of logic mentioned, differentiating between one with children and one with not – the Mishna in Horayos ch 1:4 nullifies ??? ??? ???? ????? for Sanhedrin, Rashi asks:
? ?? ??? ???? ???? ?????. ????? ?? ???? ?? ??? ???? ??????
However, the Rambam in Pirush explains a fascinating pshat:
“???? ??? ??? ???? ???? ??? ????? ????? – ??? ???? ????? ??? ???? ?? ??? ??? – ??? ????? ???? ???? ????? ???? ?????? ?????? ???? ?? ?????? ????? ??? ?? ??? ????? ????
I recall the same logic has been applied to a Chazan on Yamim Noraim, as a leKatchilah…