I’ve noticed in Hong Kong that exiters are not accorded absolute priority. That is, those entering the elevator can push their way through before the leavers have left, without being considered impolite, unlike in the United States. In part, Hong Kongers are in a hurry, but that does not itself explain the difference in customs. After all, exiters are in a hurry too, so why take away their priority rights? Perhaps we should look again to Coase. If some people who wish to enter are in a truly big hurry, they can barge forward. Furthermore, an exiter who is not in a hurry at all can hold back, knowing that someone will rush to fill the void, rather than ending up in the equilibrium of excessive politeness where each defers to the other and all movements are delayed. That is not an equilibrium you see often in downtown Hong Kong.
There is another positive effect from the Hong Kong method. If you will be exiting the elevator, you have to step forward early on and be ready to leave promptly, to avoid being swamped by the new entrants. That means the process of exit takes place more quickly. And so the entrants who are in a hurry actually do get on their way earlier than would otherwise have been the case.