@ConquistadoR @Sentinel yes, on a serious note, people exaggerate Mihawk's reaction. Going into war with someone who individually is among the mightiest on top of having a huge military might is indeed a matter of concern, especially as someone who actually isn't interested in that path. With Mihawk being portrayed as the "power" of cross guild and having a bounty of 3.6B, it establishes him as a top tier.
I still see some discrepancy with the way Mihawk is portrayed till now, not really looking great on panel till now, despite having opportunity several times. Stopped by Jozu in his attempt to aim for Oldbeard, stalled by Vista and postponing the match, stopped by Croc, most likely ending up indeed sailing on Buggy's clown ship, with his sole purpose being for Zoro, Luffy's underling, to finally fulfill his dream of becoming the WSS, which according to both Zoro and Mihawk himself isn't even Zoro's end goal anymore, when the fanbase's narrative was that Zoro will face Mihawk EOS, as Mihawk popping up in between wouldn't make sense, yet he popped out in between.
For someone who is constantly jazzed up as the top 3 of the verse, if not #1 by the fanbase, Oda did a poor job holing Mihawk up to these standards. Like, Shanks entrance alone ended the war and BB's rampage. He clashed with Whitebeard on meds, fought off Kaido, wifi diffed an admiral, obliterated the Kidd pirates with one blow, was seen as the future PK by Buggy and was Roger's golden boy, with the WG saying they would not be able to stop an angry Red Hair.