It works fine.
![Man shrugging :man_shrugging: 🤷♂️](1f937-2642.html)
And it lets them actually use all their class abilities, which is the baseline for multiclassing. You are paying full xp for each class, after all.
Removing the ability to cast in armor simulates one particular vision of a game world, but it's not one with any particular grounding in the source fiction. While wizards generally don't wear armor in the literature and that's a trope, characters who both fight and use magic (like Elric) have no issues doing so in armor, at least in pre-D&D fiction. And generally in post-D&D fiction that's not based on D&D.