No.
...and have a celestial warhorse as a class feature...(which is expensive on a realistic setting) aswell as usually have a warhorse (which is also expensive)
If you decide that a wizard "requires" a Staff of the Magi, suddenly it's a lot harder to explain why there would be any non-nobility wizards.it just doesn't make any sense to me how people of humble origins could be able to afford to be a paladin.