As a personal anecdote, I have never felt anything that I was inclined to call "willpower depletion". As a teenager, I decided that "willpower" was just a loaded term/metaphor for dynamic consistency, and that calling it "willpower" was harmful to the way people thought about themselves as agents. I decided that other people's feeling of "willpower depletion" was nothing more than sensing oneself in transition from one value system to another.

But claims that the theorized "executive system", a cognitive system whose function is almost by definition to maintain dynamic consistency, was seated in the prefrontal cortex and needed more glucose than other brain functions, made me consider that maybe "willpower" is in fact an appropriate term... but I still never actually felt anything like a "depleting resource", which I found confusing.

So I'll be less confused again if the belief dependency you mention is correct, and causal. In any case, I hope it is, so that people can achieve better dynamic consistency by not thinking of it as "expendable". I'm at least one example consistent with that theory.