This is not a restriction on the PC though, it's a restriction on the GM. "metal armor" is not defined but even under the loosest interpretation it's pretty much padded leather & hide. That's fine if we are talking about a class that can call dex it's primary or even secondary attribute, but we are not. At best dex is going to be tertiary behind wis & con.
+1 AC for "not wearing metal armor" is a class feature worth between 15 & 40gp depending on if the player settles on leather or hide armor.
That right there is a class feature with no purpose other than to troll the player & as a result puts pressure on the GM when the player justifiably angles for "nonmetal" breastplate half plate or even plate for a base unmodified 18-19+shield AC. Problems don't stop there though because 5e does not have the mechanical hooks to differentiate that +1 from a +1 on the armor a +1 on the shield a +1 on a spell a +1 on an item like a ring/cloak of protection... etc.
The whole metal armor thing is a leftover victim of 5e's quest to simplify at any cost getting rid of bonus types that made it important due to
barkskin giving a
natural armor bonus as opposed to the armor shield enhancement & luck or deflection bonus granted by
those other things. The very significant natural armor bonus stacked with all of those even if the other elements conflicted in nonstacking ways & as a result the nonmetal limitation was
not simply trolling the player like this would be.