The 3 big powers.
Marine HeadQuarters + Shichibukai System working under World Governament authority to counter balance the 4 Yonkos.
So Garp tells us that the whole Marine HeadQuarters (all marines, from the weakest one doing food to the strongest Legends, Admirals, Fleet Admiral, Supreme Admiral, Retired conselours or whatever the fuck Sengoku is doing now) plus all 7 Shichibukai (not sure if their crew is being counted here since they didn't took part at Marineford I will assume only the person) balances "perfectly" against the 4 Emperors of the Sea (the captains plus their crew/fleet).
But there is also the fear of Marines when two Yonko make an alliance that they are constantly watching them to know their steps. Also no marine (or at least Vice-Admiral level and below) has authority to engage against a Yonko on his own. So it is much unlikely that the whole force of WG (marines + shichibukais) would be equivalent of those of the 4 yonko together (imagining an alliance of them all). I'd say that WG whole force is much greater than a single Yonko (that's why none ever tried to take them alone) and probably even greater of an alliance of 2 yonkos. That's why Kaido and Big Mom even after allying with each other still wanted to go for the One Piece first before challenging WG.
Keep in mind that when WG is looking for Shichiukai they are not interest in their strenght alone. They are looking for influency.
How the balance actually works...
We have WG as the supreme, strongest organization that controls the world (or the major part of it or we could just say the organization that has most territories if compared to others). And they have their enemies that works against them which would be both pirates and revolutionaires (maybe considerated as pirates for them since they are not taking into consideration on the world balance but them not strong enough to be a Yonko crew). The world is too big and the number of pirates are too big for WG to take care of them by themselves. That's why they ALLOW the Yonko do exist in the New World since they will crush the pirates that enters those seas. And at Paradise they would have Shichibukai to help them. I guess only Doflamingo lived at New World while being a Shichibukai(and just because he had underworld connections that kept Yonkos from beating the shit out of him) and Hancock that lived after Calm Belt so not in the Grand Line (I don't know exactly what location would be that. What sea?) and Kuma that was from Sorbet Kingdom (South Blue). All those forces are used to supress people from becoming pirates and to lower the amount of pirates so WG can keep peace.
But it wasn't always like that. You see former Yonko Whitebeard (rest in peace) and former Pirate King Roger (burn in hell son of a bitch selfish dad) used to be hunted by marines that wasn't even of the highest caliber. During Oden's flashback we saw basically fodder marines going after Whitebeard (which made him leave) and Roger (which he crushed and asked for Garp/Sengoku next time). And Whitebeard explained that was useless to crush them because they would keep sending more after more (although they didn't sent one after Roger crushed during the 3 days he fought Whitebeard).
And we know that Roger's death was what caused the great era of pirates with many people going to the sea becoming pirates to find One Piece. So it is safe to say that we didn't had either Yonko or Shichibukai System before Roger's death. That's why marines stopped hunting Yonkos (we clearly see this with Whitebeard) and also why they started to allying with pirates making the Shichibukai system.
I would also say that the only reason they went to war with a Yonko was because Ace was too much of important to be left alive. If he wasn't son of Roger or if they've captured any other pirate without any blood related to Roger they would probably just freed him to avoid a war against Whitebeard since they benefits from the Yonko system.
Also the reason why Buggy and Luffy became Yonko despite the downfall of Kaido and Big Mom (although still alive) they are the ones with most influency after that event. Luffy already being called Gonkou previously fits perfect the spot. Buggy being told to have 2 ex-Shichibukai as underlings made him the other perfect candidate despite having Law and Kid there with Luffy dethroning 2 Yonkos.
So when the WG changes the Shichibukai system with the Seraphim they believe they will manage to have as much strength as the Shichibukai had to counter the Yonko that's why they made sure to have them going after the ex-Shichibukai while also having the influency of scaring people from going into piracy that's why they look like the ex-Shichibukai.
In my opinion it was a huge mistake for WG since they basically changed 6 for half dozen (Brazillian expression not sure if you guys use it there too) or even worse since they may have lost some Seraphims to Teach's crew now. Would be much more benefitial for them to use Shichibukais plus Seraphim to crushe the Yonkos and having Seraphims doing the job of Yonkos or even if they wanted only then crushing the Shichibukai and then being the only and supreme force controlling the world.
