This reminds me of the design space filled with feats that granted +2/+2 bonuses to a combination of two skills in the 3.5 era, and how we all loved that...
I think the major issue there isn't really the design space as such, but that the +2/+2 feats are incredibly sterile, and even "spiritually" worse than feats which are sterile in only a single way. It almost feels a little insulting they didn't just make a feat that grants +2 to any two different skills, with a little boilerplate to make sure one can't stack such things endlessly.
I think the proficiencies will be freebies in a lot of feats, rather than proper features. I don't give it much mechanical weight, anyway. You only need heavy armor proficiency once, from any source, and the balance implications are usually minimal -- more about flavor than raw power since the game is designed to be balanced whether one is wearing light, medium, or heavy armor. In any case, proficiencies are perfect grist for a downtime training system, as you guys have already noted, and putting it in feats could be more of a convenience.
Personally, the feats I most like are the ones that define a new way to approach play, although a strong thematic hook is always nice and usually complementary. I like Vyvyan Basterd's approach to making feats generally address more than one pillar in some way, as long as we don't follow that principle to the point of requiring absurd mental acrobatics on every feat. With these thoughts in mind, my first draft of a "heavy armor" feat might look like this:
ARMORER
Prerequisite: Medium Armor Proficiency.
Benefits: You gain proficiency with Heavy Armor. Whenever you take slashing, piercing, or bludgeoning damage you can choose to reduce that damage by an amount up to your Constitution modifier and apply it to your equipped medium or heavy armor instead. You can repair normal wear-and-tear (including damage caused by this feat) on a single piece of armor during a short rest, and also adjust its apparent condition (from pristine to banged-up) without affecting its functionality. A carefully chosen appearance may grant a +2 bonus to certain ability checks during interactions with other creatures. Your comfort in armor of various conditions grants you <some rule for reducing or eliminating fatigue from armor, probably related to Constitution.>
This would rely on a simple item damage mechanic, although in short encounters tracking could probably be handwaved. I like the implied story that you are strategically allowing the armor itself to be banged-up, and have learned to endure without loss of functionality a level of discomfort (per hit) given by your Constitution. The story is also more-or-less cohesive over the different pillars. The total amount of reduced damage in an encounter (or some other time period) can be determined by the armor rather than the Con modifier, but having high Con lets one use the power more flexibly and faster. In long fights there might not be much difference in total damage mitigated (it eventually saturates), but in short fights higher Con is definitely better. This feat incentivizes characters to find very sturdy armor, which might introduce tradeoffs related to materials/enchantments/etc. that other characters don't consider.
Anyway, my 2 cents.
