If you're really wanting to boil it down:

Iaido Fighting Style
You gain a +2 to Initiative.
When you draw your weapon as part of an attack, you can add your proficiency bonus to the damage of that attack.

Here we have a bump to initiative (every combat) and a static bonus that scales up to 3x dueling, however the draw restriction means you can get that bonus on one attack only every other turn due to action economy, 2 attacks if you have dual wielder feat, but if you're doing that, the 2weapon fighting fighting style would be prioritized...

If I made it a feat

Iaido
Prerequisite: Dexterity 13
You gain a +2 bonus to initiative rolls.
When you draw a one handed weapon as part of a reaction, you may add your proficiency bonus to your damage with it. On a hit, you can sacrifice subsequent attacks you can make this turn to deal an additional 1d12 damage of the weapon's type per attack.

This, I think, is a solid draw for fighters, but also for multiclass rogues with extra attacks...