MIhawk individually against kaido alone? I don't see any reason why not to be honest. I am of the school of thought that mihawk even today is actually a match to good old shanks, kaido's fellow yonko. Regardless of whether he wins the guy should be able to be a match.So when Shanks attacked Kaido and his army of Zoan users, he did ok for himself because Beckmann, Roux, and Yasopp can take on Kaido?
Yes, a Yonkou's crew is important and part of why the WG fears them, but it takes more than a strong crew to attack Kaido and come out in one piece. Do you think Mihawk can go 1v1 with Kaido?
Jinbei may have had a crew at one point, but it doesn't seem like he did as a Shichibukai. More importantly, when they were called to Marineford, it was them called for, not their crews. Boa and Doflamingo fought alone. The WG wants them, pardoning their crew is just a perk of the job. Buggy getting the bat for his crew is the exception, not the norm.
I don't think buggy's shichibukai deal was any different from the other shichibukai. Even luffy would have been spared from trouble by fujitora had law bothered to word things differently IIRC.

