I never let my wizard go into melee combat, so it never occurred to me to let him dual wield anything. But. If this works, does it mean a magic user could wield a staff and the defender flail, not to use the latter in melee, but to have the permanent +1 AC ?
Yes.
But at that point, you may as well just equip a shield for +2 or +3 AC...
Usually the benefit for dual wielding on a magic user would be things like dual wielding Staffs for their Spell Attack/DC bonus. Or having a Staff and something like Knife of the Undermountain King (For extra crit and rerolling of 1's for damage - An effect that gets better the more dice you are rolling, such as with higher level spells)
But yes, Duel Wielder on a caster can be useful so you can hold 2 different stat sticks, simply for their passive boosts.