I'm not 100% sure the training does enough to tone down the Wizard, as he and the Siren are still the only mages without a triple cost school, and his abilities are still tops in terms of power level and usefulness. Wizard's Tower nerf is big, though, as it means a Tower-based Wizard has to put some points into his toolbox of attack spells, not just include 1-2 of each of a wide variety of spells. In fact, he might be more likely to run an Elemental Wand to save on sbp's on the attack spells he casts himself since his Tower is going to be burning through sbp's at a much higher rate.
There are a lot of interesting consequences to the training change, though. Others have pointed out how it indirectly makes the Warlock and Warlord and Siren better, since they're the only mages specialized in Fire, Earth and Water, respectively. This means Hurl Meteorite and Golem Pit are now much more likely to be in a Warlord's book than a Wizard's book - although a Wizard could still pull it off, just not cheaper than a Warlord anymore. In other words, a Wizard is no longer a better Warlock than the Warlock, or a better Warlord than the Warlord, or a better Siren than the Siren. But he can still dabble in those things, or specialize in Air (and currently be the only mage who does).
This also means that Dragonscale Hauberk just got a lot worse - or at least, less of a must-have in multiple copies in every book. Before, there were more Fire mages than any other element (well, except Earth, but Warlord isn't as popular as Warlock in most Arena metas and Earth doesn't have a damage type so your choice of chestpiece isn't relevant vs Earth). Given that you could face either Warlock or the possibility of a Fire Wizard meant you should preferentially choose Dragonscale. Of course, even a Water or Earth Wizard generally sports a few Fireballs and/or Flameblasts, and an Air Wizard may very well continue to do so, but at least Fireballs are less likely to be spammed from the Wizard's Tower. And since the Wizard has training in Air, suddenly Wind Wyvern Hide and Stormdrake Hide are much more viable. For an armor-heavy mage, I could see having 2x Dragonscale, 1x Wind Wyvern and 1x Stormdrake... or just whatever's in school (except maybe Bearskin) and a couple Elemental Cloaks because they're versatile.
So... yeah... the other elemental schools just got "stronger" because all mages feel a little more specialized (and various strategies now have homes outside the Wizard), and thus all the non-Dragonscale chestpieces just became more relevant. All from a pretty subtle change.
(I still think the Tower is the bigger change here. A Wizard can still pack a pretty diverse toolbox; just swap Lightning Spells into an old Fire Wizard book and not much changes - except he gets better at countering swarms because Daze/Stun/Stagger, at the cost of a little bit of raw damage).
