Piccolo is the only one training the Next Gen.

[Fantastische Hure]

Gohan (duh)
Goten & Trunks (in Boo-Saga)
Pan (Super-Hero)
Future Trunks (in-directly but IIRC in both manga & anime he could use the Masenko because Gohan showed him or taught him)

Goku & Vegeta are selfish, but Piccolo trains the next gen.

 

[Spiral-Force]

If the criteria is Buu and onwards as is implied by OP. Bare minimum: Goku or Vegeta wouldn't be opposed to training with Gohan, and actively encourage it, pointing to his potential as a key reason. Vegeta doesn't have the connection Piccolo or Goku have with him; what more can he do without applying force?

Beyond bare minimum, particularly Goku: He wasn't a living warrior for a significant period of time, and Elder Kai's training was more important during Buu rematch prep. Goku encouraged everyone to train after that menace was dealt with, and by Super, was up for sparring with Gohan.

 

[Fantastische Hure]

But even after Freeza he wasn’t training with Gohan that good until RoSaT training.

 

[Fantastische Hure]

& Vegeta does not at all care to train with Trunks & Goku doesn’t care to train with Goten

 

[Spiral-Force]

Is there any example you would point to that depicts selfishness on Goku or Vegeta's part?

Would you say Goten, Gohan, or Trunks aren't at all responsible for not training harder or more often with others that train hard such as G and V?

 

[Fantastische Hure]

Literally, Goten & Trunks want to train but Goku & Vegeta (Vegeta specifically) never want to get them involved either. At-least they could help them train, right?!

 

[Symbiote]

Literally, Goten & Trunks want to train but Goku & Vegeta (Vegeta specifically) never want to get them involved either. At-least they could help them train, right?!

In the Buu arc when Gohan went get his gay superhero costume from Bulma she said Vegeta trains Trunks to make him stronger than he (Gohan) was.

 

[Spiral-Force]

On top of that, Super suggests that Goku is up for sparring with Goten as well, given that they tried to sneak away from Chi-Chi to train.

I think there are different factors as to why we don't see it more often, but would argue it's a stretch to say it's plain selfishness. Given how far apart post-God Saiyans are compared to everyone else, plus their own responsibilities of preparing for universal threats and such, kudos to them for still finding time to practice with their sons. It also ought to be mentioned that the younger boys probably prefer play-fighting amongst themselves, or being up-to-no-good with Pilaf and co. And that mini arc in Super were Gohan tries to regain his fighting senses suggests he wasn't exactly yearning for training and battles beforehand.

 

[camdudetenger2018]

well since goku is not always around since in dbz hes been axed a couple times and then db super he went to live on another planet

so piccolo is like kakarott aka gokus second in command aka number 2

and yes krilian is still kakarott aka gokus number 1

 

[ahill]

Maybe Piccolo feels lonely meditating only, so being a teacher at least gives him a sense of duty and purpose. Since he can't be the strongest anymore (he would train to be competitive and the best, but Goku and Vegeta got to a point they aren't reachable) I'd say he sees helping the new generation satisfying in the sense he has a purpose. He was even crying of happiness being grateful Gohan talked to him like a friend when no one ever would when he was about to die in the Saiyans saga, so he likely felt really loneliness... And without a goal, having someone to protect or help might matter to him.