I have found that while generals can compete with assassins early game, in the late game the assassins all have AoE abilities that can wipe out my whole minion fleet late game making them less useful.  Perhaps generals are meant to be early-game pushers but I haven't seen any games where they were powerful enough to really push hard and fast early on (the towers are too strong to push past that early).

Perhaps all that is needed is for minions to scale up more so a pure minion general doesn't have all his minions wiped out by a single AoE spell from an opposing assassin.  Another option would be to give generals (who focus on minions) some alternate end-game ability that is unlocked by taking all the minion spells.