Honestly I'm baffled that neither Goku nor Vegeta have offered to train Trunks yet, or even that Trunks himself has requested it. It's in his best interest to grow in power, and if anyone deserves the kill on Black, it's him, as he's the number one person who's been fucked by Black.
Not to mention that, becoming stronger also means being better prepared to handle future threats to his world. It's the second time he's awfully underpowered compared to an enemy that's pretty much devastating his planet. If not for Kaioshin's information on Dabura and Babidi, there's a chance even they could have done a lot of damage, or even kill Trunks. Let's say he doesn't train and reach higher levels now. His father or Goku kill Black, hurray, the future is saved again. A year later someone as strong or stronger than Black shows up. What, is he gonna time travel again for help?
While I have enjoyed Super (ignoring inconsistencies helps a lot), the fact that it's pretty much the "Goku and Vegeta" show is quite annoying, especially considering the circumstances surrounding Trunks.