I have blogged about it in the past (in May 2013) and would like to revisit this again to see if the general community opinion has changed, now that we have been revealed of Issho's true intention for being an Admiral.
Firstly, let me state how I view the "Three Great Powers" and where the Shichibukai stand in this. Note that here I am commenting based on the power levels up to pre-TS, before the resignation of Sengoku, Garp and Kuzan and Sakazuki takes the helm of and "beefed-up" the Marines.
Without the Shichibukai faction, the Yonko (meaning any one of them, not all or combination of any of them) faction was actually stronger than the Marines faction. Should one of the Yonko decides to make a move to assault the Marines, the latter will not survive. WG decided to absorb in a few individuals of pirate status who were crazy strong and / or legendary to help Marines balance the tip of the power struggle, and in return grant pardon and special privileges to the said individuals. The combination of these individuals were able to bring about a balance to the Yonko - Marines battle (in favor to the Marines of course) and thus born the faction called Shichibukai, owned by the WG. Therefore up to the time of the admirals Akainu, Aokiji and Kizaru, they still need the Shichibukai for the reason stated just now.
Imagine the Marineford war without the Shichibukai faction. The Marines don't have Mihawk, Hancock, Doflamingo, Kuma (as well as the Pacifistas), and Moriah and the rest of the canon storyline applies - Whitebeard and his allies + Luffy and his ID escapees gang. How do you think it will end up?
Yet, because the Shichibukai only has a dotted line reporting to the Marines, not often do they adhere to the instructions given by the Marines, to the point that some may totally go against the instruction or may even turn against the Marine itself. See how Hancock behaved during the war. And let's say we have Shanks vs Marines, Mihawk withdrawed from the latter or may even join Shanks (who knows). Should Kaido face off against Marines, Doflamingo may (just a thought) act similar as Mihawk did.
So in my thoughts above, the Shichibukai is actually more of a wild card, without their presence the Marines will fall and/or suffer seriously severe casualties. Should they side the Marines, then the war is equal but should they take a stand by the Yonko, then the earlier mentioned will also prevail.
The above is my personal opinion and my own take of the position of Shichibukai stand in the Three Great Powers. You may or may not agree but it serve as justification of what I am about to mention next.
Now, I based on two facts gathered from canon manga to date:
1) Sakazuki has been strengthening the Marines during his tenure
2) Issho's objective to eliminate the Shichibukai faction
I have a gut feel that Sakazuki sees eye to eye with Issho on that one, he ain't have no love for the Shichibukai individuals. Therefore he would like his Marines to be as strong as the Yonko, to the point of deeming the Shichibukai unnecessary in the power struggle. This will then remove what I mentioned as "wild card" and be totally independent in their fight against piracy. Still it only mean Marines can take on a fight against one Yonko at a time, combined two or more or all of the Yonkos will still pose a significant threat to the Marines (the same goes to Marines + Shichibukai combination), luckily enough all of the Yonko ain't no buddy-buddy and go hang out over a beer and talk about crushing the Marines.
If I were in Sakazuki's shoes, that is exactly what I will do (getting Marines to be as strong as a Yonko). A dozen of Admiral ranks that rivals the division commanders of the Yonko instead of just a small handful of three only. Then discard the troublesome Shichibukai faction instead of having to depend on them. That may mean the Marine force will be able to subdue or defeat the likes of Mihawk, Doflamingo, etc on their own, thinking about this potential is a scary thought.
All in all, from a strategic point of view and Sakazuki's absolute justice stance, I agree that the Shichibukai faction should be removed.
Sorry for the long read, did not realize the blog was so lengthy as I compose away...
Have a good day.
EDIT: In a nutshell, if I am to assign a number as the power level of each factions, it will be:
- Yonko (each of them respectively) : 10
- Marines : 7
- Shichibukai : 3
Effectively giving the equation of Yonko (10) = Marines (7) + Shichibukai (3)