Cause Mihawk’s started to get excited about the wider world again for the first time in years.
Mihawk before now was bored. He hit the top, lost his rival, had nothing to do so joined the Warlords. The balance of powers also meant to One Piece world was relatively peaceful at the start of the series, and had been for years. In the New World the Yonko were fairly established. The Warlords were all in place. The Marines were led by Sengoku, who basically kept the peace. Mihawk basically sailed around aimlessly and didn’t even bother to show up to Warlord meetings.
Meeting Zoro and Luffy excited him for the first time in years. He agreed to go to Marineford because that was something genuinely interesting. He spent the timeskip training Zoro. Now something really interesting is happening, the Warlords dissolved, while Zoro and Luffy are also hitting top tier strength, so Mihawk finally has something to look forward to.
It’s not mystery what Croc gets, he gets an absurd amount of strength.
Hierarchy wise, it’s Croc making a lot of day to day and general decisions about what Cross Guild will do… but Mihawk will do what Mihawk wants to do. Basically, Mihawk has zero interest in leading or taking charge, we know that. But Mihawk can also end Croc in a second if he wants to, and that gives Mihawk a rather large say when he choses to use it.
The disrust is very interesting. Croc’s been talking about Alabasta about how he doesn’t trust anyone, even his own organisation. Think probably his crew ran away and abandoned him when he tried to fight Whitebeard. Mihawk is a lot more interesting because we know so little about him.