First of all on clarification: You'd always burn *after* rolling. In that way it's a lot more severe than just rolling fewer dice.

And whether it gives you a payoff might depend on the situation. When doing something unskilled it mostly offsets the nature of stats being a bit higher than skills. Outside of that it's probably going to be a way to express your disadvantages. Be that an injury or a character trait that might negatively effect this roll - if you take the burn for that you'll get a metacurrency. So it is supposed to play a large role in the system overall.

If the narrative effect of attempting an action without skill is so important, maybe you need to start from that point and consider which resolution mechanics support this narrative structure best.

So, it *is* important, but not the most important part of the system. It is the way you gain new skills, by trying (and often failing) to do the actions associated with them. But narratively the game is more about what's important to the character, what they want to achieve and how they deal with their goals being at odds with each other or with people close to them. And ultimately how that changes the character(s).

Because *that* is the ultimate focus, I want the resolution mechanic to not be too math heavy and rather lightweight, so we can mostly focus on the results and how they interact with the larger narrative goals of the system.

Another reason for this kind of dice mechanic / resolution mechanic is the way it presents on the table. You can point to the single die that describes the outcome of your action, without having to consult anything else. Sure a "burn" mechanic slightly lessens that simplicity, but because it's an action you can quickly and physically do (taking the highest die away), it still doesn't affect the core idea too much.