We must hope that people don't use it. Otherwise they'll put Gregorian on dates that aren't Gregorian and Julian on dates that aren't Julian and we'll have chaos.
Hopefully we don't have any proleptic Gregorian, since nobody else uses it.
We still don't have a name for the dating system universally used by American and British historians, genealogists and reference books, namely, Julian day/month combined with so-called "historical" year.