You armor isn't "carried in one hand" when equipped like a shield, though, is it?
Most shields were held one-handed, without a loop to put your arm through (which came later). Viking shields were made to be dropped because the fibers of the wood used would "hug" a weapon lodged in it, making it difficult to be withdrawn. So, because they were made to be dropped, they were held "in one hand" without a strap for the arm.
View attachment 262933View attachment 262934
FWIW, loops were added for
cavalry shields IIRC, freeing the shield hand to hold the reins of the steed while the other hand held a weapon, while still allowing for a benefit from the shield.
Smaller loops (as in the red circle shown above) was used for hanging the shield (on walls, boat sides, etc.) when not in use, although I suppose you could slip your hand through it for extra security, but even
that shouldn't require your action for the round IMO.
It should mean you gain no DEX bonus to AC nor a shield,
then apply advantage because you are literally
not defending yourself at all! The only protection you have is whatever armor is worn, which might prevent an attack from injuring you.
Yeah, the designers favored simplicity over logic--I know that--but even in 3E WotC had different AC values IIRC (like flat-footed, which should be a condition in 5E IMO).
Even if shields in your games have straps, you can still drop them if you aren't carrying them in your hand (holding it) as well (so they are braced against attacks). The difference being it would hang from your shoulder/arm instead of falling to the ground. Either way, it is still "dropped" and no longer equipped or benefiting your AC because you can't
use it.
IMO, it shouldn't be an action to doff a shield anyway, at worst a bonus action maybe, even if strapped. Either way, you can drop it because it is carried in one hand.
If your shields don't have a strap (such as the Viking round shield, Roman scutum, or many other shields throughout history) dropping it should be a free action, as should picking it up.
View attachment 262939
(back of Roman scutum shield)