I like the tournaments but they are a pretty challenging design to get right.
The main problem as people said is the AI. Without their equipment being a factor, if you are reasonably competent at the game, it's very easy to win, even when your character is low skill. The battanian 2h tournaments are the easiest to win, since the last few rounds usually have a 2 hander that won't bounce on armor. The 1h /shield empire ones can be rough if the other guy has high tier armor, you have to focus on hitting the head or thrusting for pierce damage and it could take several rounds. The harder ones to win imho are the team fights. If your team melts and you have a weapon you aren't doing much with right away, you get into some 1vX's that take a lot more work to win.
It's hard to justify a mass melee though as the final fight. I like the idea of how they mix up your teammate becomes your opponent and things like that, but I don't know it always works in practice. I'd love to be able to enter with a companion as a teammate and just win together without fighting. But in the end the biggest and hardest tweak will be getting the AI fighting better, esp high level lords.
The other thing is the frequency of tournaments. I have a feeling when you ask for nearby tournaments it looks at the closest cities and makes sure that at least 2 of them are having tournaments. So that means you can have unlimited tournaments, which isn't a bad thing, however it makes them not important, or at least shouldn't be important.
I think I sort of hate the practice melee fights, the way enemies come running out one at a time, and why don't I get to be the guy that comes out the door last, kills one guy, and gets 250 gold? Basically it's really gamy, and if you have the time, you can just sit in a corner and let the AI kill itself and get your 250. I don't mind it's existence, but I think it could be better.
What might be nice then, is to follow the suggestions for tournaments in this thread. Make them bigger, more expensive, and more rare, and more rewarding. So there might be a huge entrance fee, you have to bring your own equipment, they only happen rarely etc. That's the big lords tourny.
Then add a second type of tourny, this is the local circuit that happens as frequently as it does now. It doesn't have huge rewards, it doesn't cost anything to enter, the area's are smaller, the opponents are bad, everyone has default gear, the reward is small, but there are rewards for lower place standings, runner ups and 3rd place rewards maybe. The idea would be that by doing local circuits you get some small amount of renown, gold, and some mid level gear, enough to start trying to compete in major tournaments.
In dreamland, (and come mod tools release time, I am thinking about trying to make this) I'd love for wandering tournament person to be an entire path of playing the game, like being a trader or playing the lords and armies game. I'd love to see basically a gladiator game packed in to bannerlord. Manage a team of fighters, pay for training, salary, tournament entry fees, manage tournament renown. Have reoccurring opposing teams/players to go up against, try to work your way up into the bigger arenas with large cash prizes etc.
But that's sort of dreaming, right now I think I'd love to see the major tournaments getting a rarity and reward overhaul, and introduce starter tournaments as a path for the player to get some mid tier gear/gold/renown help get started.