I partially disagree with both of you. Yes, a PRC is supposed to improve specialization, no it shouldn't damage generalization, however, that only means that a Class x/PRC y should have the generalized abilities of Class x+~1/2 Class y, because they trade some of that new generalization for specialization. Therefore, the trade off for the Archmage is viable, given that it gains additional casting as well as abilities, the cost of those abilities is absorbed by the additional casting.