About ruling 1d3 and damage
Short answer, no it likely won't break anything. This is easier to get, but weaker than unarmed fighting style and less versatile than a level in monk.
There is little reason to use this unless it's all you have. And if it's all you have, you are in an interesting situation. Enjoy it.
I have no argument against brass knuckles. I'd even say: makes them 1d4 to match daggers. They are weapons after all! And even at 1d4 they are worse daggers.
It's kind of weird they are not part of the base game.
But know that just giving 1d3 for being in heavy armor is not RAW. And I'd argue against giving it for free. In part because realism: armor is made to deflect blows and prevent a blade from biting into the skin, not to harm others by conducting bludgeoning force. In part because armor is protective and letting a piece of equipment be both protective and offensive is not how the game work.
It doesn't break the game, but know that you are setting a precedent at your table. Most the the rest of this answer will be about gauntlets.
What you're describing is just an unarmed strike
If we are talking pure RAW, punching someone with a gauntlet is just an unarmed strike. Nothing is said about any kind of equipment affecting unarmed strikes in the rules. (Accept individual magic items) The following quote is from this answer (referenced as PHB page 195).
Instead of using a weapon to make a melee weapon attack, you can use an unarmed strike: a punch, kick, head-butt, or similar forceful blow (none of which count as weapons). On a hit, an unarmed strike deals bludgeoning damage equal to 1 + your Strength modifier. You are proficient with your unarmed strikes.
Full plates are not mentionned in weapons rules, neither heavy armor nor general armor says anything about offensive capabilities. Even spiked armor is not described any differently form any armor. It is the Barbarian subclass that allows a battlerager to attack using his armor. Which implies that the game is not meant to work this way. From the Battlerager subclass description:
When you choose this path at 3rd level, you gain the ability to use spiked armor (see the “Spiked Armor” sidebar) as a weapon.
Considering armor as improvised weapon
Staying in the RAW territory, you could rule the armor as improvised weapon. You are free to give them any damage die. And as pointed above, 1d3 is not going to break anything.
But you are potentially leaving the door open to someone saying they are kicking with their boots, and can thus apply for improvised weapon.
What I'd suggest at my table
Punching with a gauntlet is fine as far as balance goes. But to avoid setting a precedent and to keep the distinction between unarmed and improvised clean. I would ask at least one of those things:
- A specialised gauntlet. Made to withstand being used to repeatedly punch things.
- Those unarmed strikes are only beneficial against certain enemies. Such as silver gauntlets against werewolf. Or against acidic oozes.
- Special training. A week or a month of downtime + training cost to say "this character knows how to harm others with the pointy bits of his armor"
- There's a possibility of breaking the armor. Likely a 1-in-6 as part of the damage roll (with 1d3, that would be 50% chances when you roll 1 damage).
Those last two are based on how I run my game: my players have to use some downtime and gold to do things already, so telling them they need to stop adventuring for a month is a common occurance. Also, I have no problem telling a player that they have lost the use of an arm until they spend some time repairing their armor. I also have no problems with players spending downtime to train for fighting classes and other things that are usually class abilities.
So adapt what I propose as you see fit. If time is not a factor and you don't want random failure, then the only thing someone needs is to declare that they are thinking about punching with their armor. Which anyone in heavy armor should do. But it's not gamebreaking.