The thing I've always liked about robes on a wizard is the availability of pockets for all kinds of arcane trinkets and consumables, as well as easy spots to grab spell reagents (as a free action, note that I'm thinking of my days as various D&D casters, hehe).
They're also warm and they don't impede movement unless they're particularly elaborate or long. If they go down to your ankles they should be good.
Another major benefit is that they're very quiet compared to a lot of other clothes, so sneaking around takes much less additional effort.
In general, robes aren't a dumb idea for wizards. It's not just a trope. It's an incredibly practical option in some settings (I'm using D&D to make my case of why it should be taken seriously because it's what I know).
Now, A shirt and pants with a couple satchels or a pack and a satchel would do a good deal of the same things as a robe. It can just be more cumbersome, even if it is more stylish in some views.
