"... blah, fluff, blah, you must be proficient with the armor you are wearing to cast a spell."
Means, unless I missing something, Mountain Dwarves are the only armor wearing wizards (by RAW and presuming no multi-classing). With multi-classing and super low XP for 1st level it is eminently min-maxish of any Wizard to take a level of Fighter.
Now, DMs are free to plug this "hole". It's just weird (still assume I missing something somewhere...) Although, maybe armor is not a big deal with all the "impossible to die" rules (full hp regen every night, partial hp regen rests, multiple saves before death, lots of spells to auto-make saves / heal / be not dead, healing potions in the equipment list, etc.).
Personally I like Dwarves to be the antithesis of magic and Elves to be fighter/mage types. I'd house rule Dwarves to have advantage on saving throws against magic and be unable to take Wizard levels. And Elf Fighter/Wizards being one of the very few multi-class options available.
[wtf is up with basic PDF jacking cut and paste?]