Is there any good reason to focus on "All Skills" for any of the training regimens? (Well, except for maybe Fitness & Tactical).

Attacking: Agility, Footwork and Carrying might be useful for all offensive players, but a RB or WR doesn't need passing (unless you're Antwan Randle El) and a QB doesn't need catching ... (at least I am assuming)

Defending: Again agilty can be useful for everyone. But blocking and tackling are completely different skills. They are opposite of each other.

Kicking: Unless you want an all around kicker, it would make much more sense not to do all skills.

I guess Tactical could have use. As would Fitness.

I believe you have answered your own question

Fitness is a good one to train "All skills" but some of the skills have a hard cap - Ofcourse, you can only see this when you are a Supporter.