Clarification would be welcome, since we're almost certainly not using the term willpower in the same way.
I'm using it to mean relying on conscious choice in the moment, to overcome preference reversal. Forcing yourself to do something that, at that moment, you'd prefer not to, or to not do something, that you'd prefer to.
What I do instead, is find out why my preference has changed, and either:
Remove that factor from the equation, either by changing something in my head, or in the outside world, or
Choose to agree with my changed preference, for the moment. (Not all preference reversals are problematic, after all!)
From that usage your claim makes much more sense.
Willpower in my usage is more general, when impulses are overridden or circumvented. In your example, it includes the conspicuous consumption of which you describe, but also more subtle costs like the cognitive computation of determining the "why" and forestalling the impulse to remove internal or external factors.
My main point is that willpower is a limited resource that ebbs and flows during cognitive computation, often due to changing costs. But it can be trained up, conserved, and refreshed effectively, if certain hazards can be avoided.
I've often had half-finished LW post ideas and crossed them off for a number of reasons, mostly they were too rough or undeveloped and I didn't feel expert enough. Other people might worry their post would be judged harshly, or feel overwhelmed, or worried about topicality, or they just want some community input before adding it.
So: this is a special sort of open thread. Please post your unfinished ideas and sketches for LW posts here as comments, if you would like constructive critique, assistance and checking from people with more expertise, etc. Just pile them in without worrying too much. Ideas can be as short as a single sentence or as long as a finished post. Both subject and presentation are on topic in replies. Bad ideas should be mined for whatever good can be found in them. Good ideas should be poked with challenges to make them stronger. No being nasty!