I think that maybe it would make sense if playing with a cub can give it training experience? If you read the text for training a cub in cub training, they're basically just playing anyway, and play is how cubs learn in real life. I know there's a chance of gaining a skill stat for the cub when you play, but it doesn't help much if you can't get your cub to a high enough training level.

tl;dr
Playing with cubs (and maybe adolescents) should add to the training bar

Edit: maybe even tussling instead of playing because that's a little rougher