I could not find any major TP savings by training in a skill through the ASC system instead of the normal training point system.

For the first 5 ranks of ASC, based on the normal post-cap TP cost of 2500 exp. for 1 PTP and 1 MTP, Warriors training in Mental Lore and Monks training in Elemental Lore are better off training through the ASC system than through the normal training point system. For Clerics, Empaths, Sorcerers and Wizards, the cost of training in Dodging through normal training points and ASC training points is the same. For Warriors, the cost is the same for Sorcerer Lore. I doubt many Warriors and Monks train in those lores, but I am certain that post-cap Clerics, Empaths, Sorcerers and Wizards sometimes train in Dodging.