1) This would literally be Deus Ex Machina out of nowhere, singing was never portrayed like that;
We don't dismiss things simply because they're deus ex machina. And regarding the second part, like, the singing has already been portrayed that way (in the context of singing = power).
Like, the first episode has a scene where Lilith is described as empowering demons with her voice and music.
And WOG explains that this scene isn't about emotional power, but about real power.
And before you say "why don't they sing all the time to amplify their power?"
We know it amplifies, but not by how much or how it works. We only know that several overlords and seraphim singing and combining their powers were enough for 5-B.
2) Hazbin’s broadaway force was always portrayed as your typical musical. Singing being literal is stupid;
One thing being stupid doesn't contradict anything.
Yes, they sing all the time, but what does that contradict about singing being an amplifier?
3) They never use it during fights;
Isn't that an argument? 99% of the characters on the wiki don't use all their powers in combat; we don't ignore powers because they aren't used consistently.
Like, seriously, Alastor has some things in his P&A that he doesn't use in combat. Like fire hax, he's never used it, so let's remove it then? He can also teleport people, why hasn't he ever used that in combat? Seriously?
Besides, for your argument to work, the characters have to be aware that singing can actively serve that purpose. They might be singing because they like to sing without being aware of this active amplifier (which is normal because these characters sing in all sorts of situations for no reason).
3.5) Assuming they don’t know about the singing amp, they are not surprised they stopped such a threat despite being 9-A fodders;
The characters are currently 8-A, not 9-A.
Furthermore, why would they be surprised? In terms of the statement, that bomb only had the power to destroy half the city; we're just assuming it has more power than that.
Besides, being surprised or not by something doesn't mean much. The characters' reactions or what they think aren't absolute truths about anything. If an ordinary sinner looked at Adam and said, "Nah, I'd easily defeat you with a single finger," you'd give him the same tier as Adam because "well, this guy is very confident he'd defeat Adam and isn't afraid." Actually, we don't do that, otherwise Alastor would already be in tier 7.
If you think the characters' reactions matter so much, then why did Husk, the FTL/5-B, react by hiding behind a car when some radar guns fired at him with ordinary firearms?
4) Rosie & Alastor scene are heavily implied to be Rosie asking for Alastor’s help because he is strong, not because he can sing and has some magic. She could’ve just lended some nobody souls so he can have bare minimum magic and get singing amp from there;
Alastor is helping because he's strong and also because he's another person singing, which helps with amplification.
There's a difference in power between 14 tier 8 people amplifying each other and 14 tier 10 people amplifying each other. Having more strength helps because it receives more momentum through an amplifier (like math).
5) Emily downscales from Lu normally as Seraphim (Rosie implies that rankings in Неаven show power. And don’t bring up Vox restraining her, Alastor restrained General of Exorcists via magic too, doesn’t mean he is stronger), but with the sixillion amp that buffs 9-A to 5-B she should’ve simply stopped it herself;
If Emily downgrades Lucifer, and she's normally 5-B, then it worsens the explosion feat, because now it wouldn't be a bunch of 8-A receiving an amplification, it would be a bunch of 8-A and 5-B receiving an amplification and stopping the explosion.
Furthermore, again you assume they know exactly the mechanics of musical amplification + the argument of "if they have this power, why don't they use it?"
Characters having various powers and not using them all the time, or not using some powers in the most efficient way possible, is the most common thing that exists. Unless you think we have to remove powers from P&A that aren't used all the time or in the most efficient way possible.
6) AWs > heavily beaten up General of Exorcists (don’t think it’s drop him to literal 9-A), and near-100% Vox managed to scratch cell of Lucifer while Vaggie’s AW didn’t.
Adam was seriously injured and attacked from behind by surprise; it's not really that serious.
Besides, angelic weapons aren't currently accepted as such a significant power boost, otherwise the hotel staff would be 7-C with angelic weapons, which doesn't fit their profile.