Simplified Armor

The following table replaces the armor table and rules for wearing armor while non-proficient in the PHB

Armor Type	Armor Class	Mobility Disadvantage?	Stealth Disadvantage?	Spellcasting?	Cost
Basic	11 + Dex	-	-	-	10 gp
Simple Mail	12 + Dex	Yes	-	-	30 gp
Martial Mail	14 + Dex (Max +2)	Yes	Yes	No	60 gp
Plate	15 + Dex (Max +2)	Yes	Yes	No	200 gp
Shield	+2	-	-	-	10 gp

Basic ["Light"]
Congratulations, you're wearing something that's more protective than just the clothes on your back. This is the consolation prize of armors — you're probably going to want to get something better if you can.

Shield
Ah, a nice slab of wood or metal that you can put in between you and someone trying to disembowel you. If you aren't using a shield, you're either really confident or really poor.
Special: You can't cast the Shield spell while wearing a shield — you can come up with your own in-world explanation for why, but this is purely a balance consideration.

Simple ["Light"]
You've upgraded to proper armor. This is the bare minimum of what can be expected of someone who fights on the regular — and people will behave accordingly.
Penalties: If you don't have light armor proficiency, you have Disadvantage on Strength (Athletics) and Dexterity (Acrobatics) checks while wearing Simple armor.

Martial ["Medium"]
Now we're talking. This is what you're generally going to be wearing if you're a professional — soldiers and your better-equipped town guards are going to be wearing Martial armor.
Penalties: If you don't have medium armor proficiency, you have Disadvantage on Strength (Athletics), Dexterity (Acrobatics), and Dexterity (Stealth) checks while wearing Martial armor.
Familiarity: If you have medium armor proficiency, the maximum Dexterity bonus for Martial armor increases to +3, and you can cast spells while wearing Martial armor. If you have heavy armor proficiency, you may use your Strength in place of your Dexterity when determining your AC while wearing Martial armor.

Plate ["Heavy"]
This is a sign that you're rich, my friend. You're basically a walking pre-modern tank. This is what the elite wear.
Special: As long as you are wearing Plate, you are immune to critical hits from non-magical weapons. If you're wearing magical Plate, you are entirely immune to critical hits, regardless of their source.
Penalties: If you don't have medium armor proficiency, you have Disadvantage on Strength (Athletics), Dexterity (Acrobatics), and Dexterity (Stealth) checks while wearing Plate.
Familiarity: If you have medium armor proficiency, the maximum Dexterity bonus for Plate increases to +3, and you can cast spells while wearing Plate. If you have heavy armor proficiency, you may use your Strength in place of your Dexterity when determining your AC while wearing Plate.

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Some further suggestions:

• Dwarves never have Disadvantage on Athletics and Acrobatics checks due to wearing armor. Go Dwarves.
• If you start with scale mail or better, you start with Martial armor. Otherwise, you get Basic armor. Druids start with non-metal Martial Armor.
• On that note, Druids can find non-metal versions of everything other than non-magical Plate armor.
• Armorer Artificers can use Intelligence for AC while wearing Martial or Plate arcane armor.
• Barbarians, Monks, and characters with the Natural Armor feature get to use their "unarmored" AC while wearing Basic armor — it that Basic armor has a magical bonus to AC, you get to stack that bonus on top.
• Similarly, Monks can use Martial Arts and their Unarmored Movement bonus while wearing Basic armor.

...

Thoughts?

Looks alright to me, though it appears you have Plate worded with medium armor proficiency under penalties and familiarity. Copy/paste error?

Edit: This is also a straight buff by removing STR requirements (while also adding ability to dump dex) and stealth disadvantage when proficient, negating Crits in the case of heavy armor. Not an overwhelming one but worth noting.

Nope, that's not a typo — it's effectively half-plate if you aren't proficient in heavy armor, and plate if you are.

Those buffs were intentional, honestly — though the Strength requirements are effectively there because you need a Strength of 14 to match chain mail/splint, and a Strength of 16 to match splint/plate. If the partial crit immunity ends up feeling excessive, I might just make that require heavy armor proficiency.

I don't think it'd break anything, but I do question if it's needed. Put another way, I wouldn't use this in my games, but I'd not have issues playing in a game with these rules.

Is this just a "I like it more" tweak, or do you feel this addresses issues in the game?

You should tidy up the table. Describe what you need to remove the disadvantage, or restriction.

Armor Type	Armor Class	Attribute to AC	Athletics Disadvantage?	Acrobatics Disadvantage?	Stealth Disadvantage?	Spellcasting?	Cost
Basic	11	+ Dex	-	-	-	-	10 gp
Simple Mail	12	+ Dex	-	Light	Light	-	30 gp
Martial Mail	14 + Dex	+ Dex (Max +2, +3 with Medium)	Medium	Medium	Medium	Medium	60 gp
Plate	15	+ Dex (Max +2, +3 with Medium, Strength with Heavy)	Medium	Medium	Medium	Medium	200 gp
Shield	+2	-	-	-	-	10 gp

Basic ["Light"]
Congratulations, you're wearing something that's more protective than just the clothes on your back. This is the consolation prize of armors — you're probably going to want to get something better if you can.

Shield
Ah, a nice slab of wood or metal that you can put in between you and someone trying to disembowel you. If you aren't using a shield, you're either really confident or really poor.
Special: If you have more than one Shield, only gain the largest benefit, don't add them. The AC boost from Shield spell counts as a Shield.

Simple ["Light"]
You've upgraded to proper armor. This is the bare minimum of what can be expected of someone who fights on the regular — and people will behave accordingly.
Penalties: If you don't have light armor proficiency, you have Disadvantage on Strength (Athletics) and Dexterity (Acrobatics) checks while wearing Simple armor.

Martial ["Medium"]
Now we're talking. This is what you're generally going to be wearing if you're a professional — soldiers and your better-equipped town guards are going to be wearing Martial armor.
Penalties: If you don't have medium armor proficiency, you have Disadvantage on Strength (Athletics), Dexterity (Acrobatics), and Dexterity (Stealth) checks while wearing Martial armor.
Familiarity: If you have medium armor proficiency, the maximum Dexterity bonus for Martial armor increases to +3, and you can cast spells while wearing Martial armor. If you have heavy armor proficiency, you may use your Strength in place of your Dexterity when determining your AC while wearing Martial armor.

Plate ["Heavy"]
This is a sign that you're rich, my friend. You're basically a walking pre-modern tank. This is what the elite wear.
Special: As long as you are wearing Plate, you are immune to critical hits from non-magical weapons. If you're wearing magical Plate, you are entirely immune to critical hits, regardless of their source.
Penalties: If you don't have medium armor proficiency, you have Disadvantage on Strength (Athletics), Dexterity (Acrobatics), and Dexterity (Stealth) checks while wearing Plate.
Familiarity: If you have medium armor proficiency, the maximum Dexterity bonus for Plate increases to +3, and you can cast spells while wearing Plate. If you have heavy armor proficiency, you may use your Strength in place of your Dexterity when determining your AC while wearing Plate.

It does look like you meant to say Heavy on Plate?

Honestly, I personally don't like it. 5e already pared down armor to the bare bones, this just feels egregious to me.

You should take a look at an RPG called Five Torches Deep, it is mostly a simplified version of 5e, it's armor set up is almost exactly the same as this. It's lower powered than standard 5e though.