Was there ever any intention for the Hell's Kitchen heroes to pop into the MCU? It's clearly the same Universe, but the whole point of the series (aside from more nifty stories) appears to be to tell super hero stories in a small, local scale, which is a direct contrast to the movies all being city, country, or world-spanning arcs.
Maybe the Spider-Man movie could bridge that a little bit I guess since he is focused in the streets of New York as well, at least to start with. As much as it could be neat to see the crossovers more directly I dunno if it makes any sense from a storytelling or grand scheme perspective. Even Agents of Shield is basically not referenced in the movies still and that has way stronger ties to the MCU movies.
Edit: Just looked at Night Nurse on Wiki, it sounds like Claire Temple (from DD/JJ) was originally just going to be Night Nurse but they went with a different name and more of a composite character. So if they're casting a Night Nurse for Dr. Strange, then either they could roll with it as a group of nurse friends or just have Dawson be her own thing.