If Khan doesn't move to the US he'll never improve
Khan flies over to the UK after every fight and chills out for months. What this means is that everything he learns with Hunter he will start to forget because he's not going to the gym regularly working on his technique.
Consequently, he'll have to relearn everything for each fight so it means he will always remain at the same level and never really improve. He'll be stuck at the crossroads so to speak, but never quite getting to the other side because the techniques aren't getting engrained into his brain. As soon as he learns something he leaves the country and starts to forget.
That's why the only option for Khan to improve is to move to the US and be close to his trainer, like any normal fighter.
I think Khan is stuck in the schedule of training that he had while he was with Roach but the difference now is that a new trainer is trying to teach him new things so in order to effectively learn those things he needs to spend much more time than before... A change is gonna come.