I once asked a room full of about 100 neuroscientists whether willpower depletion was a thing, and there was widespread disagreement with the idea. (A propos, this is a great way to quickly gauge consensus in a field.) Basically, for a while some researchers believed that willpower depletion "is" glucose depletion in the prefrontal cortex, but some more recent experiments have failed to replicate this, e.g. by finding that the mere taste of sugar is enough to "replenish" willpower faster than the time it takes blood to move from the mouth to the brain:

Carbohydrate mouth-rinses activate dopaminergic pathways in the striatum–a region of the brain associated with responses to reward (Kringelbach, 2004)–whereas artificially-sweetened non-carbohydrate mouth-rinses do not (Chambers et al., 2009). Thus, the sensing of carbohydrates in the mouth appears to signal the possibility of reward (i.e., the future availability of additional energy), which could motivate rather than fuel physical effort. -- Molden, D. C. et al, The Motivational versus Metabolic Effects of Carbohydrates on Self-Control. Psychological Science.

Stanford's Carol Dweck and Greg Walden even found that hinting to people that using willpower is energizing might actually make them less depletable:

When we had people read statements that reminded them of the power of willpower like, “Sometimes, working on a strenuous mental task can make you feel energized for further challenging activities,” they kept on working and performing well with no sign of depletion. They made half as many mistakes on a difficult cognitive task as people who read statements about limited willpower. In another study, they scored 15 percent better on I.Q. problems. -- Dweck and Walden, Willpower: It’s in Your Head? New York Times.

While these are all interesting empirical findings, there’s a very similar phenomenon that’s much less debated and which could explain many of these observations, but I think gets too little popular attention in these discussions:

Willpower is distractible.

Indeed, willpower and working memory are both strongly mediated by the dorsolateral prefontal cortex, so “distraction” could just be the two functions funging against one another. To use the terms of Stanovich popularized by Kahneman in Thinking: Fast and Slow, "System 2" can only override so many "System 1" defaults at any given moment.

So what’s going on when people say "willpower depletion"? I’m not sure, but even if willpower depletion is not a thing, the following distracting phenomena clearly are:

Thirst

Hunger

Sleepiness

Physical fatigue (like from running)

Physical discomfort (like from sitting)

That specific-other-thing you want to do

Anxiety about willpower depletion

Indignation at being asked for too much by bosses, partners, or experimenters...

... and "willpower depletion" might be nothing more than mental distraction by one of these processes. Perhaps it really is better to think of willpower as power (a rate) than energy (a resource).

If that’s true, then figuring out what processes might be distracting us might be much more useful than saying “I’m out of willpower” and giving up. Maybe try having a sip of water or a bit of food if your diet permits it. Maybe try reading lying down to see if you get nap-ish. Maybe set a timer to remind you to call that friend you keep thinking about.

The last two bullets,

Anxiety about willpower depletion

Indignation at being asked for too much by bosses, partners, or experimenters...

are also enough to explain why being told willpower depletion isn’t a thing might reduce the effects typically attributed to it: we might simply be less distracted by anxiety or indignation about doing “too much” willpower-intensive work in a short period of time.

Of course, any speculation about how human minds work in general is prone to the "typical mind fallacy". Maybe my willpower is depletable and yours isn’t. But then that wouldn’t explain why you can cause people to exhibit less willpower depletion by suggesting otherwise. But then again, most published research findings are false. But then again the research on the DLPFC and working memory seems relatively old and well established, and distraction is clearly a thing...

All in all, more of my chips are falling on the hypothesis that willpower “depletion” is often just willpower distraction, and that finding and addressing those distractions is probably a better a strategy than avoiding activities altogether in order to "conserve willpower".