Well how would you suggest you deal with a busy station, you get told you are number 7 in the queue - are you going to sit hovering and count the ships leaving?
What about ships that launch after you? Will they wait until you have gone?
If you leave early will that confuse the NPCs and cause them to stay hovering?
Do you think that the hovering ships should have their departure number displayed so you know which one to follow?
Sorry, to me this is not "quality of life" - this is "busywork 'cos I had an idea".
In the end, as long as players are not penalised for ignoring it, then fill your boots.
You can choose whether to wait your turn or just fly out and weave through the NPCs whenever you see an opening, just as you can decide whether to obey the speed limit coming in and out of the station.
The NPC ships would generally wait their turn, though it would be nice for their AI to have a bit more variation in character, with some of them being a little rebellious.
Whether or not they would stay hovering in confusion if you left early would be a function of how well their AI is programmed.
I think a better implementation than having departure numbers displayed on the waiting ships would be to have your HUD display your place in the queue, and prompt you when your number is up.
Whether or not it's a quality of life improvement as the OP suggests is not as relevant as whether or not it would be a good addition. I think it would be from a practical sense, as I don't think a station would have such a haphazard departure system in place, particularly since they're so stringent about docking and entry. It really should have been there from the start, and adding it now wouldn't have any negative impact on play.
As you say, there's no penalty, so there's no constraint on players. It's just an added touch of realism, though as I stated in a previous post, it may come in handy in situations where there are a lot of actual players in the station.