The kiss is about memory transfer.
Gabriel put his memories into a fly--why can't Crowley give his memories to Aziraphale? This is why Aziraphale looks so strange in the elevator: he's experiencing Crowley's memories--of the two of them, of the way they love the world, and whatever they mean to each other.
Maybe this choice, to give his memories to Aziraphale, is a last ditch effort on Crowley's part to persuade him to stay. Maybe it's something more strategic. Let's say he knows Aziraphale won't change his mind. What can he do to help him?
He can't go. I'm not convinced the heavenly host wouldn't kill him, or that the change back to angelic status wouldn't destroy who he is. He doesn't want to be an angel anyway.
But, if Aziraphale goes with Crowley's memories, he goes with Crowley's perspective: what he's experienced and who he is.
Without that balance, Aziraphale is prone to blindness to heavenly injustices. That's the point of the Resurrectionist historical sequence, and many other scenes. He wants to believe that good is good, despite any evidence to the contrary. Crowley's signature cynicism--and his trademark mercy--will be with him.
Did Crowley give so much of himself that he'll forget Aziraphale and all that they mean to each other? He does look a little deflated as he's driving.
With Crowley's memories on board, will Aziraphale finally be able to catch up to Crowley? Will he be ready to have that all-important actual conversation about what they are to each other?
Aziraphale may have to give the memories back. Whatever this kiss meant to the two of them, with all its face-smashing, collar-grabbing desperation, I wonder what a future kiss could be?
@laughing-at-the-darkness did I forget anything?