What is really the purpose of the shield and helmet options if the max armor a player can have is 3? Less expensive combinations to get to 3 armor, but take up more slots than just heavy armor? That's the only real benefit I can see, but the gold difference is minimal, and there's no cons to chain or plate - though I guess it would be reasonable to put disadvantage on stealth when wearing chain/plate.
Even thou additional rules for armor types aren't explicitly written, you'll always fallback to the Fictional Positioning: maybe you can say it is Impossible to be stealth with a heavy armor, or flee from an unarmored foe.
The Disadvantage case is also covered, as you just need to consider the PC as poorly equipped.
In these examples, I think it is all the GM's preference, so no futher rules are needed imo.
One last example you'd want extra pieces of armor is with the Scrap Fighter ability :P