Well the wizard in D&D is the most versatile class, he has no limit in how many spells he can learn and those spells go from illusion, mind control, damage, flying, divination, shapeshifting, and the list goes on.
The saving throws are there as check and balance, without those a lvl 3 wizard could kill anyone given initiative. At low levels it might be a bit frustrating but once you reach level 5 wizards start to shine, and after level 11-12 they become a force to be reckoned. Even after the reduction in spells and spell power that we have in 5e. A wizard is still the most powerful class at high level, because of the sheer versatility.
