"Willpower" is just another facet of attention. I claim it's easier to do deep work when not in a cluttered, crowded, overly-warm workspace with unasked for music, a dynamic precluded by the purely-incentive based model you're falling back on.

You actually /can't/ just weigh the tradeoffs of being disctracted and reach a decision of not being distracted.

No -- it's meaningfully and sustainably easier to make good decisions when bad options are removed from the table (sometimes literally.)