Where it falls apart is with the assumption that only the poor have to make difficult decisions. If anything, wealthier people spend a lot more time making decisions at work and receive commiserate cognitive load. Not sure working at McDonalds requires you to make any decisions at all.
Even if we're going to pretend that financial decisions are the only decisions in life, I still think the poor might expend less cognitive energy. Frequently they are poor because they specifically avoid making financial decisions. (Hence that's not a cognitive load.) On the flip side, people with more significant assets have to make more significant/difficult allocation decisions, etc.
You also have to remember that for many people in a service role, that might be the only job they could find and they don't have the chances we do to pick and choose roles based on interesting projects.