On a meta level, Good Omens S3 was EMOTIONAL ABUSE.
... Meaning, I'm pretty sure Neil Gaiman did it ON PURPOSE, knowing how much it would upset the fans.
Neil knew how badly we wanted Aziraphale and Crowley (OUR version of Aziraphale and Crowley---the specific version of them we met in Season 1) to be together. He knew we wanted to see them resolve their issues and ultimately choose to be with each other in the end.
Instead, Aziraphale and Crowley forgo that emotional journey in favor of unnecessary pain. Neither of them experience real character growth in the finale; they are shown to be the worst and unhappiest versions of themselves, without getting a real shot at redemption. They never fix their communication issues. They don't express their true, authentic feelings for one another (don't @ me with that bullshit hand kiss thing). They never manage to get on the same page emotionally---even when they both agree to commit suicide (which I'm pretty sure was not the "one thing" Aziraphale wanted).
"Why give me Crowley? Why make me complete and then take it away?"
EMOTIONAL WITHHOLDING is a common abuse tactic utilized by men like Neil. They enjoy creating ATTACHMENT in their victims and then "TAKING IT AWAY".
It's easy to see how much Neil enjoyed frustrating his fans in retrospect. He actively taunted us on social media with the catchphrase "WAIT AND SEE" and threatened to make Aziraphale and Crowley kiss---but in a way we "wouldn't like". He loved dangling the implied promise of a happy ending over our heads, which we now know he never planned to deliver on.
Neil was unkind to his audience. He was also unkind to his characters. Aziraphale and Crowley are treated as punching bags throughout the entire series---shown to be "messy" for the sake of entertainment, but not as a real obstacle for either of them to overcome. God herself says she enjoys seeing how much Aziraphale values his relationship with Crowley. And this turns out to be her justification for "taking it away". (Tell me THAT isn't some fucked up shit.) Aziraphale and Crowley experience real emotional pain as the result of her actions---and this is demonstrated by the incredible acting of Michael Sheen and David Tennant.
Neil explicitly sold this as "a love story" when he created the show. Based on the tone of the book, an eventual union between Aziraphale and Crowley would have made the most narrative sense. It would have emphasized the overarching themes of love, agency, and the futility of "choosing sides". But that would have required Neil to possess the same ethos as Terry Pratchett---meaning LOVE AND RESPECT FOR FELLOW HUMAN BEINGS.
We were never going to get a good love story out of Neil. Men like Neil get off on "PUNISHING" people for no apparent reason; he obviously did this with our beloved characters, to disastrous result. Nonetheless, we still manage to ascribe deeper meaning to Aziraphale and Crowley, thanks to the phenomenal acting team and the dedication of this fandom. Aziraphale and Crowley remain the greatest love story of all time, not because of anything Neil actually wrote, but because of everything that was projected onto them by the people who cared. We assigned their relationship a depth "Neil himself" never could have imagined---one that exemplifies our maximalist ideals of love and the decision to choose it again and again, in spite of everything. It is never going to "end" on Neil's preferred terms. In this rare instance, fan interpretation STILL MANAGES TO ECLIPSE THE SOURCE MATERIAL---and that is because LOVE is always a more powerful story than ABUSE.