Why not back up a step? There aren't even rules for blocking with a shield or your armor. Rules for defense would be interesting. As it stands, your AC doesn't have anything to do with blocking - it's just a number that prevents you from losing your "durability, the will to live, and luck" (i.e. hit points). Blocking would prevent armor damage, wounds, and pain. If holding a weapon is effectively holding your durability, will, and luck, then sure; let the weapon add to AC.
You need to use a lot less luck/durability/will to turn aside a blade with a sword compared to using your forearm. (Unless you're a monk) - so yes: that's exactly what I would like to see.
Somehow. Mechanical details matter, but the lack annoys me.
Edit: for example, something like (assuming 5e):
"When holding a simple melee weapon with which you are proficient, you may set your AC to 11 + the weapon's ability modifier.* When holing a martial melee weapon with which you are proficient, you may set your AC to 12 + the weapon's ability modifier.*
*The weapon's ability modifier is the ability modifier you use for attack rolls with that weapon, normally strength. You can still add applicable modifiers the you AC, such as from shields, spells, magic items, and fighting styles."
Slightly bad for Barbarians (as it makes their Unarmored Defense redundant), might be a little too good for Hexblades as written. But it's not getting you higher numbers than you could already get, just giving you the option of leaning on blocking rather than armor per se.
In 3e/PF1, I'd probably just use a feat tree with really low introductory prereqs or something. For 4e/PF2 I'd either do that or add armor-alternative class features.