In my experience, in both Arkansas and Georgia (both US Southern states), this has always been the norm at work. If there are men at the front, they get off first, but if there are multiple men near the back, the one closest to the 'door open' button holds it and the women get off first. Women just 'know' that we move to one side or the other, near the front, and then fill towards the back from there. I've never had it not work that way, in the years I've been working.
In other places, it's first come, first served - and yes, it would be a bit creepy in hotels or apartments. But I've seen it consistently in offices in the US South, and it is nice, especially if your elevator is one with a very fast door cycle.