ehh .... I don't know about "Training" it, like doing a big block of front squats.
But seems like most lifters just do them here or there through out the week, a few reps, intensity not volume.
I get what you are saying, if you can increase your front squat, by back squatting ... so be it.
But besides just improving the clean recovering (obvs), front squats also improve a lot of the positional strength, and leg drive of the jerk.
In my opinion, back squats don't improve those as much ("per unit of energy" put forth into them).
If you have no time for front squats, you might be able to work them in with cleans every now and then.
Clean + FS + Jerk (top set of CJ? just omit the FS)