Why would Mihawk join this shitty organization in the first place?
What do you mean shitty? We just need Doffy and we will have the most charismatic group (and Buggy) in OP. I think this chapter is good for Mihawk fans. Don't listen to idiots who are saying Mihawk wants Buggy's protection. Also, I think Mihawk joining the organization will be comedic, not anything he actively decided to do. But if he did, the name "Cross Guild" pretty much indicates that it's Mihawk's group (unless there is some other meaning behind the name that the spoiler providers aren't telling yet).
I would've preferred him to stay out of this whole throne war and wait for Zoro till he matures. But that is not happening. So, this is the second best option.
I will wait for Redon before judging this chapter. As bad as everything else has been about Wano, this development may genuinely be good.