Honestly that book is a bit overrated from an ancient point of view and many of the so called "wise" quotes from it would be glaringly obvious to any competent military commander; "know your enemy and know yourself" of course, no one goes into a battle without knowing the enemies usual tactics, composition, and strategies they used in the past because that's how Carrhae happened.
Though part of me suspects the book was mainly to teach the absolute basics to weak aristocrats who got their positions from nepotism or other connections. Romans would probably read the book and laugh at it.
Traditionally Roman military learning was just that, book learning interspersed with on the job training, the change to the academy system would indeed weed out some of this, however what books would they learn from other than their own and others military literature. unless there was some conscious effort to produce new military manuals (there you are talking about the number of wealthy enough people who liked writing) for that school system. naturally you would employ military veterans as teachers however how would you go about educating the children of Senators, Equestrians etc? I think this has been discussed but I cant recall in which chapter?
on another note I hope that the decisive battle that is planned shows off some of that lovely siege tech hinted at by Hectatee. plus I am thinking prepared positions, plenty of stakes, flame fougrasses (amphorae filled with flammables ignited by either slowmatch or maybe copper wire/electrical device?) plus pre-deployed caltrops to funnel cavalry to pre-defined fields of fire? strike down the barbarians........