I hadn’t picked up on this the first time I read the rules, but is it fair to say that Training skills essentially represent a binary “can/cannot” type of situation? You never test something like Armour Training, right? What advantage does practicing it to higher ranks bestow the character in question?
Correct.
You don’t train it to higher levels. Once you have a training skill, you “know” it. You never roll it, so you don’t gain tests, and practice does not earn you further tests either.
The GM could always add new training skills to represent specialization or whatnot, but that’d be strictly house-ruling.