Blackbeard;
—> Crosses into Paradise with two weak subordinates to take the most hax fruit of the verse.
—> successfully ambushed a 3b pirate and utterly defeats them with only a few weaker subordinates.
—> sends his men out to Egghead to pick up Vegapunk.
Mihawk;
—> Too afraid to go ahead with Crocodile’s plan, “muh manpower”.
—> Visibly afraid of entering the race for the one piece.
This dude is allergic to screen time
He simply knows he isn't strong enough and doesn't want to gamble like BB. BB could be ok with staying as Shichibukai as well, but he didn't, he risked everything to get more.
The guy was ok with living rest of his life with baboons and chasing Don Krieg, and getting stopped by Croco when he actually decided to hunt PreTS Luffy and apologized from Shanks. He is not taking risks.
Its interesting how Buggy forces him to do it though, thats the fun part. Buggy shows more courage than Mihawk.