I do agree with most you said, but this situation is different
Shichibukai System was completely removed, it's just that there were only 4 Members to deal with
But in such situation, they could have had to deal with Seven !!
So obviously the order wouldn't be to send One Admiral for each Member
They will simply send multiple Battleships & this entire operation will be led by a Single Admiral as Supreme Commander & multiple Vice Admirals leading each Attack, & Fujitora is the one chosen here
And i believe Fujitora is sent for only One Shichibukai & that is Hancock, simply for Three Reasons:
1. She is only Shichibukai who cannot Sail away since she is Royalty & must protect her Kingdom
2. She have a Powerful Nation under her command so they must be Stopped, unlike Mihawk & Weevil who are Alone & Buggy who mostly have Mercenaries who can abandon him once he loses his Shichibukai Privileges
3. Because out of those Four, Hancock is only one who abused her Title & disobeyed WG multiple times, such as helping Luffy multiple times