[loup-vaillant]

Short term, it probably does make things worse. There are studies about limited willpower, like when you measure the patience of people by having them performing a chore, the control group have more patience than the group that where explicitly forbidden to eat that cookie over there.

But doing it every morning is different. First, by making it a habit, you don't need as much willpower as you did the first times. And if it trains willpower, then the long term result will likely be better than doing nothing.

Similarly, when you exercise in the morning, it leaves you more tired for the rest of the day. Your muscles may even ache the following morning. But do it every (other) day, and it (i) won't be that tiring, and (ii) you'll be in better shape anyway.

[mikeash]

"And if it trains willpower, then the long term result will likely be better than doing nothing."

This is the key. Does it train willpower? Is it like physical exercise? Or does it just deplete, with no benefit?

I can see the reason for thinking it might be a benefit, but without actually showing that it is, it seems wrong to just assume.