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?
Mihawk is actively excited about the prospect of being hunted right? He says so himself
It defeats the purposes of his excitement if he's just going to go make an alliance to avoid his excitement.
Rayleigh alone was a big enough threat as one man that the government STILL couldnt afford risking their forces to deal with him. Mihawk is one man and stronger than rayleigh and doesn't have political leanings of any kind. The government won't shill out multiple Admirals to deal with mihawk at the risk of losing even one of them
The best the government will do is maintain a steady amount of pressure to maybe get him to leave his Island and it's actually possible Mihawk just shows up in the new world with like five marine battle ships trailing him like 1 kilometer away.
Again, Mihawk doesnt care that he's being hunted. He actively welcomes it. The government also will not actually try that hard to capture hum since once again he has no political ideology yet he's like one of the strongest in the verse.
Your argument that the plot requires Mihawk to ally with shanks is built on contrivances. It's contrived that Mihawk suddenly fears for his life. It's contrived that Mihawk would join a political side while not being political himself. It's contrived that Mihawk even has this sort of relationship with shanks in the first place.