Once Ryze gets Tear of the Goddess and is getting access to blue buff, his mana problems in the early game will disappear. When he hits lvl 6, he'll be able to use his ult to help sustain his health and he can use it often thanks to the part of his passive which lowers his spell cooldowns by 1 everytime he uses an ability. The health you get back from ulting and firing spells at minions and champions scales with levels and items; the health from Smite spell vamp not so much.
Ignite is useful for the entire game not only for the damage but also the 50% healing reduction; something that I think would be mandatory if you were facing a Dr Mundo on the other team or a Vlad or Swain in lane.
All in all, the benefit of Smite is a pretty temporary one that is not quite as useful as other masteries such as the 10% magic pen that scales with the amount of magic resist the enemy gets from items like Abyssal Scepter, Aegis of the Legion aura, Guardian Angel, stuff that the AP carry may be benefiting from.