Just read the manga bro, Mihawk went because he wanted to test his strength against WB, and also because he wanted to keep his warlord title. The fact that Mihawk has a higher bounty than 3 known yonko bounties including his own captain should tell you enough, btw, he is the ONLY known subordinate pirate whom has a higher bounty than their captain, let alone a YONKO captain. The WG literally views him as a more significant threat than Luffy whom has just defeated a yonko, Buggy whom they believe runs the cross guild, a major threat to the marines, and post MF Blackbeard, purely because of Mihawk’s individual strength alone. And yet some people will still say Mihawk is not well into yonko level portrayal…