Using joy-cons, it works for me. Are you sure you’re holding A? That is, whatever is mapped to NES A on your controller (the “jump” button).
Edit : also, if I remember correctly that only brings you to the beginning of the world, not specific level. So if you were on 1-4, you’re still going to 1-1.
I just tried with my 8bitdo (not a pro controller though, SN30 pro). Game over on 3-2, A+start brings me to 3-1.