I think it the reasoning in Basic/BECM was two-fold.
1. simulation of LOTR. The above quote from Fellowship aside. Dwarves are skilled craftsmen and hearty warriors : leading to the Dwarves=Gimli trope.
and 2. A balancing check against the "Elves are magic-users/have spells." So we made Dwarves, not only not magic-users, but highly resistant to magic...by way of saying why, in their multitude of battles and wars with Elfkind, they weren't just steamrollered with spells.
So then AD&D-and on just continued to carry this forward. Til the "everybody can do everything is core" of 3e.
...and yes, it's still a thing. As long as D&D is originated by Gary GYgax and based heavily off of LotR, Dwarf Wizard will be "against type." You whipper-snappers have another 30-40-some years 'fore those of us who started on Basic or 1e are all dead. So after that, you can make/claim the tropes whatever you want them to be.

hahaha
To lend my hat to [EDIT Oops: it was [MENTION=6731904]SirAntoine[/MENTION] . Sorry @
Kobold Stew /EDIT], I have certainly banned them outright for many many years. Nowadays, I'm getting soft in my middling years, and if someone came to me and wanted to be a wizard dwarf, I'd allow it and they would understand they are/will be an oddity and not well-received/-viewed in dwarven or wizarding circles.