Nice theorycrafting there with 2x agility formula.
Let's compare the effective dodge/evade (synergized) skill at
level 20, with varying armor penality, agility values all through 3 - 15 and how new Nimble formula (2 x agi for both AP reduction and bonus) compares to the current one (flat 15%). For this purpose I made an Excel sheet with the exact formula: Base dodge/evade skill at level 20 is 110 with every agility point above 4 providing 8,5% bonus. The 10% malus at 3 agi doesn't apply because it's offset by the synergy between the two skills.
Bold purple values indicates that only Nimble AP reduction applies with no skill bonus (total armor penalty is not at zero).
Requiring minimum of 5 or 8 agi for various 10% and 15% AP armors just for full Nimble bonus might be too much. This would only tip the favor more towards the metal armors. Most builds require min 6 str already: Pistols, snipers, ARs (7 for Full Auto feat), gloves (7 for feats like Wrestling and Bone Breaker) so in most cases it would still be better to invest 1-2 stat points in strength and go for metal armor, instead of extra 2-5 in agility for a Nimble-able light armor.
Maybe the 12+ agility formula would actually be better. In that case 8 agi for ancient rathound leather armors is still pretty high. Any build will miss those extra points somewhere else so it's not without a price.
I don't think that the issue is actually with light armors or Nimble. It's just that metal armors are way to powerful and really need a nerf. Maybe by giving them a cth malus of lets say 10-agility %. That way agility would be relevant to them as well.