My two cents on Kaido.
I think he's been an interesting character. I believe the most important trait about Kaido is that he's bored. He's the strongest thing alive and he has been on top of the food chain for years. He can't reach the One Piece (at least not in a short timeframe) but he also has no real challenge. So, in his general lack of excitement, he spends his time trying suicide and getting wasted while he rambles on about wanting to get a glorious death.
From this perspective, I think him getting fired up when Luffy offers him a good challenge and enjoying the fight makes sense. Keep in mind he's also stronger than Luffy still, and he's 100% sure he'll come out on top. He's still playing. We haven't seen desperate Kaido yet. This and his sentimental drunk phases have been fun character traits that give him a little more nuance than just being a typical evil mastermind or just a mindless brute like Jack is.
Then there's another trait about him that rounds off his character pretty well I think. Kaido is kind of a hypocrite.
His compliments to Luffy? They come from arrogance rather than from sincere appreciation for his opponent like in Katakuri's case. He has also praised Law and Zoro and neither of them was really a menace to Kaido. But they're dangerous enough to force him to be focused on the fight! That's quite a feat against Mr. Indestructible.
His longing for a good challenge? It sure is there, but only for as long as he's sure he will win. If he wanted to fight Oden so much he could have let him recover from his sucker punch and go at it again instead of boiling him to death. Even against Luffy, yeah he was sad and angry when the CP0 guy interfered but he shrugged it off pretty quickly.
And even his longing for a glorious death may not be so sincere, he could have gone up againts the WG or against Whitebeard at any time if he was so serious about it. But he prefered to stay in his skull island getting wasted.
On top of all this he has enslaved an entire nation for twenty years, enabled scum like Orochi, Caesar and Doflamingo and we've seen how he treats his daughter. There's plenty to despise there. He's… kinda casual about it, which is interesting imo. He's not a mustache-twirling villain that takes pleasure in inflicting pain, he's just cynical. He benefits from enslaving Wano, so he enslaves Wano. If the citizens are not okay with it, they'll rebel and he'll crush them, otherwise that's the end of the story. It also doesn't seem like he really holds grudges, he'll try to recruit any opponent he defeats instead of killing them or whatever. He uses brutal methods to break their will, but you can see he's more business-oriented than anything else in these matters.
Yeah Crocodile and even Ener were more magnificent bastards than him but it's fine if Oda tries to give more nuance to his later villains. Big Mom was not straightforward at all either and I think both her and Kaido have been interesting and generally more human than other villains.
However there's one thing that, in my opinion, didn't fully work... Kaido has been a good character but not exactly a great villain.
First, Kaido is the enabler but most of the real evil stuff was done by Orochi. So Luffy beating up Kaido doesn't feel as cathartic because nothing we've ever seen him do on-panel has been particularly despiceable. There was his speech to Momo on the cross where he gave him a choice to survive by forsaking his name that felt delightfully devilish, but not much else.
And then, yeah we don't know what his goals are. Doffy went down without us ever knowing what his plans were too, but at least you could more or less understand he wanted to overthrow the Celestial Dragons because they rejected him and he needed Law's fruit for that. With Kaido though... We don't really know anything at all. His ultimate goal, why he is in Wano, his past with Rocks... Nothing. Even though he's been fairly well characterized, if you don't know what his villain status stands for at its core, yeah it falls a bit flat.
Also, I don't really think Yamato has been a spectacular character and that ties into Kaido as well. You'd think Kaido and Yamato would have been used to develop each other as characters, but we didn't really get much from their relationship. Just Kaido trying to break Yamato's will and Yamato not bending. But not much about what they think or feel about each other. The drama between Sanji and Judge felt way more visceral, on both sides.
Finally, Kaido's gimmick of "breaking wills" helped to further flesh him out as a character, but was painfully ineffective on the main characters. He tried this on Kidd, Luffy, Killer, Yamato and Momo and it failed every single time. The only major character to fall victim to this is Hawkins and he barely interacted with Luffy.
And finally finally, his status as the world's strongest creature leading the most brutal crew didn't really deliver. He and his crew didn't take out even one character. The Straw Hats definitely struggled more than usual but it still falls a bit flat.
120 chapters with Kaido on screen, you may have wanted him to be a little more effective, or a little more brutal, or for his goals to be a little more defined. At this point I don't think Oda will deliver on everything (personally I'd want to know at least some of his past, to get some closure with Yamato and to see him actually get really angry). That's kinda been the problem with Onigashima, the plot moves but the story doesn't and sometimes it feels a little frustrating.
I'm still always hyped to read the next chapter anyways, so what Oda is doing can't be that wrong…
Welp, this turned into a wall of text. Sorry, everyone!