That would actually be comic accurate, too (to some degree). At one point, Aunt May reveals on her deathbed that she secretly knew Peter was Spider-Man for a long time, and wanted him to know that she was proud of him before she died.
They retconned this, of course, bringing Aunt May back to life with no memory of Peter’s identity. Then eventually did more stories about Aunt May learning Peter’s identity, dying, then coming back to life… man, keeping up with comic book lore sucks.