You aren't just carrying a shield in D&D though. Well, I suppose you could but if you were it wouldn't add to AC. Saying "it doesn't explicitly say" could be used justify that all your armor falls off.
You armor isn't "carried in one hand" when equipped like a shield, though, is it?
Some shields were held one handed, others had a loop you put your arm through. Viking shields fo example were mad to be dropped because they were designed to "catch" edged weapons, effectively disarming your opponent. However that also means they had to drop their shield.
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made to be dropped because the fibers of the wood used would "hug" a weapon lodged in it, making it difficult to be withdrawn.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.
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.
As far as paralyzed...how far do you take it beyond advantage? Someone on leather armor that's paralyzed should have at most an 11 AC. We don't because the game values simplicity over logic.
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).
I don't understand what people who think that you can drop your shield for free (or do it by accident when you're unconscious or paralyzed) think that "donning" and "doffing" mean. How do you drop your shield without doffing it? You somehow have your shield on the ground and yet it is still "donned"? So if you pick it back up it's still "equipped"? That's so weird (to me).
I see where you're justifying it RAW, but I don't get what is happening in the story.
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.
(back of Roman scutum shield)