@Desperado:
The idea is that they fight all 3 calamities at the same time in different places with different teams, taking them out in short time leaving only Kaido, The Flying Six, some Numbers and maybe Kyoshiro plus tons of fodder. Assuming Luffy and maybe one other person fights Kaido, the Samurai, Minks, Strawhats, Heart pirates and the army should be plenty to handle the latter.
I won't say that it is impossible to track down a moment when all the calamities would be isolated from each other and from the rest of the crew at the same time, but that's pushing it a little bit. We don't know if there would be such an opportunity or if the alliance could get this intel. For example, Queen rules Udon and Jack rules Kuri, but they spend most of their time in Onigashima or wherever else while the headliners do the daily chores.
Also, defeating the calamities should take a lot of time considering that Jack fought against Inu and Neko for 5 days (and let's not forget about the length of the fights against Cracker and Katakuri). The Beast Pirates could react against this assault sending reinforcements to the calamities while they don't go down, and it would once again become a standard battle.
Obviously, if Oda wanted to do that, he could easily create the opportunity to follow your ideas… but it's just as easy for him to say that the alliance didn't have the means to put this alternative plan into work, explaining that a lot of inconviences would make this plan impossible. Ultimately, this is an arbitrary decision by the author, and what is important is to hit the right beats of the narrative.
The fodder maybe, but I cannot recall a single greater One Piece (or shonen villain in general) going down due to untimely alcoholism. Usually it's just a minor inconvenience or makes them even stronger. See, I would agree with you if we had made the experience that large armies make a difference in One Piece battles and one army getting drunk would severly weaken the enemy forces, but usually the major battles are decided by a handful of superhumans who are mostly immune to the effects of alcohol.
It's obvious that no shonen villain will ever fall down due to alcoholism because that would be anticlimactic… but the characters are not thinking of shonen rules when they elaborate the plan. It's just logical to them that the Beast Pirates would be weakened by the booze and the festive spirit. It's a gigantic surprise attack when the enemy is known to be vulnerable.