Way of the Monk is a specialization in itself, once you pick it, you cannot go back. I mean, you can pick up weapons and armor again, but you have trained yourself to be better off without them. And so it makes sense to just have 3 levels unlike the other fighting styles. And also specializations unlock only at lvl 45, very late, and you need something until that too.There is no specialization skill for Way of the Monk, and there should be. I think adding your suggested stats to a specialization skill would be better.
Why not both? Skills are very expensive, you have to think twice and then again where to spend each point. Yet another skill is thus not the best way to improve, even if you can get the first level for just money and crystals (wich are also very rare). Also we already have Strong hit, that gives +2 AD. But maybe this "Iron fists" could give +25% Dmg multiplier for each level when fighting unarmed.How about another skill you can purchase, starting with one or more oegyth crystals (but not necessarily at Charwood!)? "Iron fists". You are trained by punching and kicking hot sand until the skin on your hands and feet thickens and becomes harder. Boosts AD.