Mihawk is very much the subordinate partner in that deal, far more than he'd be in a friendly alliance with Shanks
Because times change, and so do people. Mihawk and Shanks used to fight each other up and down the Grand Line.
Now they're both, more than anything, waiting to see what the next generation- Luffy and Zoro- can do. They're not brash young men anymore.
The world stage and the Balance of Power is also going to be in an unprecedented level of chaos now, and it directly effects Mihawk. The World Gov is actively hunting him, they have a brand new superweapon for the purpose of replacing the entire Warlords, his protege is soon coming to the level where he's going to surpass him and Mihawk is also very interested in seeing what Luffy will accomplish.
Because staying by himself doesn't advance the plot or the character in the slightest. What, are we never going to see Mihawk and Shanks together again? Is he just going to sail around in his boat, interacting with no one until he one day shows up, has a fight with Zoro and loses?