To be fair, that might've always been the plan. The beginning of Alastor's prequel comic has him killing a rose plant, one of Lilith's outfits on a portrait in the pilot resembles Rosie's, the way Alastor looked at the picture of the Magnes and the whole "Rosie never died" thing Faustisse stated in a livestream suggests that Alastor's working for Rosie=Lilith. Perhaps Alastor seeing Charlie on TV was his opportunity to get involved in her endeavors with a valid claim to being there.
But of course since S2 has Charlie meeting Katie Killjoy for the first time means that he can't use that for his explanation on how he heard about the hotel. There's also Angel Dust being taken back by Mimzy's backstory of him to which he already heard nearly word by word from Vaggie, and Vaggie getting on Angel Dust's case on participating in a turf war when her idea of a trust exercise is... having Angel Dust and Sir Pentious fight in a turf war. So for that last point, either Vaggie wasn't intended on being a former exorcist (the more likely scenario) or they would've gone about building her up as one differently since her acting as a drill sergeant in Episode 3 was the major instance of foreshadowing the reveal.
Yeah, Vaggie was definitely intended to be just another Sinner but Viv took the popular fan theory of Vaggie being a former exorcist. Kind of like how she took "Charlie and Vaggie are girlfriends".
Anyway, when you look at the original pitch bible, the show starts out relatively the same; Charlie talks to the leader of the Exorcists and learns that extermination day will be coming sooner this year, while Vaggie is attempting to make a commercial to advertise the hotel. After that episode, that's when the show differs with the pitch being about the people from the hotel and the shenanigans that happen in Hell. The seemingly last episode for the season would have been Charlie meeting with her dad and the other deadly sins, instead of a battle with the exorcists.
Also Alastor isn't mentioned or seen in any of the pitch episodes (except for the one about the commerical), so supposedly he would have less focus on compared to the other characters. Hell, Nifty has an episode dedicated to her, which we don't get in the amazon version. Husk also would get an episode focus on him and his background; Baxter would be the one to join the hotel instead of Pentious; Mimzy would join the hotel after her introduction episode instead of fucking off; Katie Killjoy and Tom Trench would come to the hotel and do a surprise interview; and Sir Pentious would have tried to woo his crush Rosie with Charlie, Niffty, and Mimzy being his wingmen. While I can't confirm this would have been better than what we got, it would have been drastically different and I can't deny that I don't have some interest to see the original vision for this show.
She's certainly a very sympathetic character, given how we saw how much she's suffering from Adam's loss based on the leaks. There is a potentially interesting character journey in there if during her quest for vengeance, she recognizes she's only bringing more misery while not resolving her own, or goes through a change of perspective if she winds up getting to know some of the people Charlie was trying to redeem. The setup's there for a classic antagonist to protagonist plot line, and is the kind you'd expect in show who's theme is supposed to be redemption.
But Viv probably wants to use her as another character to project all her personal feuds and hatreds onto like she did with Adam, Lute probably meant to represent all those girls in high school that she hated for being prettier and more popular than her.
It's even worse than that. Not only did she lose her boss which was probably the only person in Heaven to understand her, she lost her other teammates, her job, her only purpose for what she was most likely created to do, and no one in Heaven seems to care. They're only concern is this Sinner that got to Heaven which is the first time ever to have happened, and now that there will be an uprising from Hell because they now have confirmation they can kill angels, no one wants to do anything about it. Sera could even confirm this by looking at her magical floating orb but does because she's stupid.
Of course Lute is going to crash out. The one thing she has been trained all her life to prevent from happening is about to happen and no one wants to do anything about it.