So I'm going to go on a huge tangent from the other theories and go to what I think the core movement (or whatever legal term is appropriate) that got the majority vote at Reverie: the approval of mass producing Vegapunk's latest weapon.
No this isn't a sexy idea...but it's what fits the most. The key aspect is that whatever got approved at Reverie now has both Kaidou and Big Mom SCARED to the point that they are immediately willing to form an alliance and want ALL the Ancient Weapons to fight against it.
There are not many things in the world of One Piece that are this strong. I doubt Oda is introducing Vegapunk's version of the Ancient Weapons (he is too much of a goodie-goodie to give the Government the power to destroy the world). What is on this level is if every single common Marine can successfully damage a Yonkou.
Recent chapters show us that haki is the somewhat B.S. power that can negate everything. Even seemingly impossible to beat powers like Marco's phoenix-based fires are easily overcome by haki (on a side tangent, I'm curious to see how Kaidou would handle Law's Room). So even if Vegapunk could create Kizaru's lasers to be shot from a gun that any normal human Marine could use, this is still not enough to threaten a Yonkou. Defensive busoushoku plus Kaidou and Big Mom's "iron balloon" is why they do not take damage even if they are spammed with massive amounts from an elite fruit ability attack.
However, if this could be imbued with a pseudo level 2 haki (or some scientific equivalent) then THAT is world changing. Kaidou and Big Mom are so big that they continue to take significant damage even if they barge in at their full speed. If the 99.99999% of the world can legitimately damage Yonkou/admirals, then the numbers now allow for a guaranteed victory. There are still significant losses in the victory, but everyone from Kong through the lowest ranking East Blue recruit would make the same decision of a guaranteed win.
Blackbeard still feels pain, so he gets defeated through the same mechanics of astronomical numbers dealing significant damage in overwhelming volumes. Shanks is smaller, and makes it a bigger loss for the Marines (more friendly fire), but with enough numbers then even Shanks eventually gets easily defeated too.
As I referenced earlier, this is a no-brainer so everyone in the Marines make this a universal decision. I have to think even Reverie might have been a universal vote too. None of Luffy's allies are going to prioritize concern for Luffy (they have absolute trust in him already) over defeating the Yonkou.
This not only explains why Kaidou and Big Mom are acting so frantically (vs. not even fearing the admirals). This also explains why everyone (Government and Royals) are willing to abolish the Shichibukai system with zero concern.
So with this theory, we get a true "fifth Yonkou" that Luffy has to defeat. This is probably the only sexy part of the theory because it now creates the biggest "enemy" Luffy will have to take on. He will have to overcome something that makes Kaidou and Big Mom think they have zero chance of winning against even with their alliance.
Mrpremps if you can come up with some sexy twist, I don't need to be given any credit. I think all I ask is that promotion of the VCC website as the "source" of the idea.
Marco Polo I think I'm finally remembering to do this for once...