In order to restore class identity I think that schools should be given exclusive spellement upgrade paths to improve some of their signature utility spells that are normally available to all schools via training points.
Take Ice and Tower Shield for example. It's one of the most generally useful shields which is befitting of the Ice school. But because it costs 0 pips any other school can utilize it as effectively as an actual Ice wizard. The only advantage an Ice wizard has afterward is pretty slight, such as being able to have more copies of the spell in their deck.
Thus I think it would be neat if Ice wizards and only Ice wizards had access to a spellement upgrade path for Tower Shield to give Tower Shields used by actual Ice wizards a little more "oomph" compared to other schools using it. The spell would still be available to everyone via training points. Ice wizards would just be able to make their version a little better.
As far as upgrades go these spellement paths could be straightforward and may not even have branching paths. For example Tower Shield could give 55% damage reduction at tier 2 and 60% damage reduction at tier 3.
Other examples of school-exclusive utility spell upgrades could be: Satyr: increased base healing amount Reshuffle: Reduced pip cost Feint: Slight increase to damage for both traps
Spellements for these utility spells should not be primarily gated behind packs or the Scroll of Fortune. Instead they should be obtainable in a fashion similar to Karamelle spellements.
Satyr: increased base healing amount
Reshuffle: Reduced pip cost
Feint: Slight increase to damage for both traps