For some people, dbz is nothing without Goku; Goku makes the show for them. There are a lot of die hard Goku fans. But there are some people out there like myself that are open to Goku just not being around. It makes the anime interesting and less predictable; I'm ALL for that.
BUT, in all fairness, we kinda already saw a world without Goku in DBZ. The future timeline with Future Trunks when Goku passed away due to the heart virus and it wasn't pretty. I get that. But what I'm actually referring to is the Cell Saga and setting up either Gohan or Vegeta to take over, and Goku staying out of the picture for good. How would this change dragon ball z as we know it?
Well... I can think of a few things that could happen as a result.
1) Vegeta Will Lose Motivation
First things first, the way Vegeta is set up now, it is a bit ridiculous. He's not a true rival.
He never gets to handle anything without Goku interfering in some sort of shape or form. He's never allowed to shine and is forever subjected to Goku's shadow.
Vegeta is ALWAYS a few steps behind.
Don't get me wrong, I enjoy Vegeta as a character and he's one of my favorites.
Vegeta is a well-developed character and he's come a long way, but he could be better. Strength wise Vegeta lacks.
He never surpasses Goku and if he does, it's not for long.
If Goku stays gone after the Cell Saga, Vegeta would feel some type of way for sure because he'd never get the satisfaction of proving to himself that he could do it. In this case, Vegeta would never get the rival status he deserves. I think this would make Vegeta lose his motivation. Sure, he could set his sights on Gohan and surpassing him, assuming Gohan took the lead and fell in Goku's footsteps and all, but it wouldn't be the same.
And I personally think Vegeta's pride would not allow him to settle for the second best option, which is what Gohan would be to him.
Not only that, but in more cases than one, we saw Vegeta fall into a slump, get pissy or visibly bothered whenever Goku is gone. One example is the Bojack Unbound movie. Though not canon, the man was depressed! Like a man that had just got his heart broken.
2) Gohan Will Blame Himself
If Goku stayed gone after the Cell Saga, Gohan would probably hate himself. Fact of the matter is if Gohan never got cocky, Goku wouldn't have sacrificed himself. And Gohan was too smart to not be aware of that. Goku just kinda took this as an opportunity to stay gone to prevent more enemies from attacking Earth.
Honestly, this could work one of two ways, this could force Gohan to take fighting more seriously and could set him up to take on his father's roll. But the foundation for this would be guilt. Gohan is not really a fighter, but I feel like this would push him in that direction out of necessity. As long Gohan's MC Journey starts off as a necessity FIRST, I don't think it'll be out of character for him. It would kinda suck because Gohan would be only trying to look over things in guilt, but I feel like this would be a good opportunity to give some of the Gohan fans what they want.
Some Gohan fans want him to stay true to himself and not fight.
Others want Gohan to not waste his potential.
With Goku out of the way, there's room for others to grow and this would make sense.
With Goku around, he will always save the day so there's kinda no point in the other characters at times, Vegeta and Gohan included.
3) Goku Never Meets Goten
This one has to be one of the more obvious things that change, but we all know that Goku first met Goten at the Tournament. With Goku being permanently written off, that's not happening and Goten would grow up without a father. Now I don't think this would affect too much but it will affect one other thing that I'll dive into later on. (Fusion Dance)
4) No Majin Vegeta
So this is tricky, but I wholeheartedly believe that Vegeta would have no need to seek power because Goku isn't around. There's no one really around to prove anything to. Goku was his main motivator and the reason why he threw all logic to the side. This would definitely change the Buu fight as we know it and Goku and Vegeta would never have their fight. It's kinda crazy that even with the sacrifice Vegeta made with all those people and the sacrifice he made to get power, it still wasn't enough in the canon story. Because Goku had SSJ3 in his back pocket.
BUT I can kinda see Vegeta fighting Gohan here instead, which is why I said this is kinda tricky. Maybe Vegeta finally gets out of his slump from Goku not being around and then decide to take down the next best thing which is Gohan.
5) No SSJ3?
If there's no Goku to show us his SSJ3 form, we'll have no idea that it exists. We only found out about it through the Majin Buu arc when he used it against Fat Buu to stall for time. Canon wise I'm sure Vegeta always felt hoed, but he wouldn't feel extra HOED here because he simply won't know about SSJ3 either, but knowing Vegeta, he would have his suspicions.
Vegeta would just never be able to prove it.
BTW, kinda sucks that Vegeta never really obtained SSJ3.
6) No Gotenks
We talked about Goten and Goku never meeting earlier. There would be no Gotenks. Goku was the one that taught them the Fusion Dance and assuming that Goku is completely out of the picture, Gotenks isn't happening. And if it still did happen for some reason, there definitely wouldn't be a SSJ3 Gotenks. So I highly doubt Gotenks would have a fight with Super Buu.
7) No Vegito
Here's another obvious one that kinda sucks, but we wouldn't get to see the Potarra earrings. Unless maybe Gohan and Vegeta could fuse. I mean a Potarra earring fusion isn't off the table because Gohan was approached by the Kais. I'm not too sure what a fusion would look like between Gohan and Vegeta, but it could be pretty interesting.
Would the Earth Be Destroyed?
Without Goku coming back and staying permanently gone, this definitely disrupts many things including the Buu Saga. But Gohan still has a chance (as well as the Earth) and I say that because the Kai's are involved and Mystic Gohan would probably still be a thing. While it would be interesting to see either Vegeta or Gohan to take over for Goku, it'll most likely be Gohan as Gohan is Goku's offspring.
Plus I'm assuming that Vegeta is still in his funk and lost his motivation anyway, so everything kinda falls on Gohan. I feel like Vegeta sacrificing himself can still be a thing. It'd just end the same way. He could rise out of his funk and realize he needs to protect his family and sacrifice as a last ditch effort.
This could be great development for him to get over his Goku obsession and realize he needs to be strong for him family.
Meanwhile for Gohan, this could be used as an opportunity to change him. Like make him learn from his past mistake with Cell. I can still see the Kai recruiting Gohan and Gohan still becoming mystic, so I feel like the earth still has strong chances of living on. Gohan literally got cocky in his fight against Cell and Majin Buu.
I never understood why they made him repeat the same mistake with Majin Buu. In reality, if you mess up, you tend to learn real quick not to the same thing. It was kinda stupid and bad writing to make him do the exact same thing that made him lose his father. But that's just my opinion.
It's not that I dislike Goku, I just think it'd be more fun if he passed on the torch. Just like Naruto did with Boruto. I really feel that letting Goku stay gone after the Cell Saga, gets the side characters out of the mindset of "Goku solving all the problems." They're too reliant on him and I feel like this holdings them back from development.