Dude...
Roger is the one who created One Piece. He didn't find anything but some islands. He was the first to reach both Lodestar and Laugh Tale.
People called him PK simply because he travelled around all islands of the world.
Roger does have feats of course. Going toe to toe with WB, defeating Rocks with marines etc. But the title itself doesn't take any of that in consideration. Anyone visiting all islands would be considered Pirate King. And You don't have to be strong to do it. About 2-3 Red Poneglyphs Roger got without even fighting. Not sure about the first one he got.
Where is Xebec portrayed above Yonkos? He aimed to be more than Yonko or a mere PK. But I don't remember he ever being portrayed as more than that. His crew was portrayed as the strongest to ever exist.
About OP, again this is a Roger thing. Not sure but I think Roger told everything to WB. He had no interesting before and remained like that after hearing it. So how PK can be superior to someone that simply have different dream?
Mihawk already let clear that haki is a part of swordsman ship. That whole hakiman thing is fandom made. Shanks can user everything in a battle against Mihawk. You could argue that Shanks was weaker before but now he is stronger and etc. But the reallity is that Mihawk is WSS therefore he is stronger than anyone considered a swordsman just like WB was strongest than anyone considered a pirate(Mihawk included).
Even WB is running from marines and he is told to have the power to destroy the world. Mihawk doesn't need to stay where he is being target everyday just to support his title. Everybody wants peace sometimes.
There are a lot of rivals in One Piece with incredible amount of gap between them. Zoro vs Sanji. Luffy vs Kid/Law. Moria vs Kaido.
Actually he found Joy boy treasure and that either is the one piece or the central portion of the OP (if we intend it like Roger leaving all his treasures at the last island).
And even if that feat doesn't seem anything great he was the first and only one to do it. That is most likely due to voice of all things and/or other unique skills only chosen ones get. About the strength concept I agree, he was said to have run from BM but at the same time he put down Xebec and was regarded as the strongest one along with WB (and we have seen the mess an old, sick etc. WB did at Marineford, Akainu and BB were not enough to kill him, they also needed to plot behind his back, the whole crew of BB, elite marines swarming him etc.).
Xebec was clearly portrayed above a mere yonko. Like you said he probably had the strongest crew we have seen in OP under him and have WB, Kaido and BM work under him is something incredible. Also even if he didn't find the OP (probably he had not the characteristics needed for it, like when WB said to BB at marineford he was not the one Roger was waiting for, that was probably referred to the one who is fated to find the OP, and BB is also, 99% sure, the successor of Xebec will just like Luffy is for Roger) he had the power to rule the seas and even aim to become the king of the world. That for me was like if a yonko is so strong that us able to suppress all the other rivals he has and becomes the sole overlord.
About the PK I don't think he is superior to others for that, he most likely must have rare/unique skills like voat but that doesn't equal to battle strength, even if now that Luffy has been portrayed as the choosen one and get the nika asspull/df he basically has toonforce so he is broken to the point he can't lose if Oda wishes to (he just need to draw the cartoonish stuff he draw in the Kaido fight and have him brush away any attack no matter how strong) but that is also the main character, PK title pales if compared to that. To conclude I generally agree, WB didn't dream about the PK title but Oda said he was on par with Roger (yet Roger/Luffy should have some special ability like voat WB lacks)(and Luffy get absurd main character perks others can only dream off).
About the Shanks/Mihawk thing either way, this for me is almost sure, they are extremely close powerwise but if one has to trump the other that is Shanks. About the swordsman - non swordsman if you think about it Whitebeard too had a famed blade, even if that was a glaive and not a sword, but still Mihawk himself put WB above him. That means that Mihawk swordsmanship is above WB since Mihawk is the WSS, still if WB uses all his strength, haki, df, whatever he wins. Same goes for Shanks, at least for me, Mihawk is the better swordsman but if you put Shanks acoc in the equation they end at the same level. Also look at what he did to Greenbull, he scared an admiral who was miles away out of the fight, his sword gryphon was used just as a tool. And either way this is extremely good for Mihawk too, being on par with Shanks at this point means they both are well above an admiral like Greenbull and most likely even stronger than yonkos like BM or even Kaido (see Kaido putting Shanks with Xebec, Roger etc. And also at this point we can guess how Shanks stopped Kaido from coming to Marineford).
To end about the rivalries, it is true and I agree that rivalries like Zoro vs Sanji are a bit if a joke in the end but I still think the Shanks/Mihawk is a true one (rivals very close powerwise). That was made clear for me when Shanks threatened everybody at Marineford but Oda decided to save just Mihawk's face making him leave of his only accord before Shanks spoke, not Akainu, BB or any other top tier, just Mihawk. And that means, for me, he didn't want to ruin the rivalry. But, even if I don't think this is the case, if this rivalry in the end is an unbalanced one (Zoro vs Sanji etc.) I think Mihawk is on the losing side. Oda will not ditch the main character role model in favor of Zoro's, who in the end comes after Luffy for importance.