Does this mean that we should stop punishing ourselves for procrastination?

My personal experience strongly suggests that "stop punishing yourself for X" helps avoid X, for most if not all X. For instance, becoming a vegetarian was much easier when I didn't try to go cold turkey, but rather was fine with the fact that I would succumb to the lure of eating meat every now and then. When I did, I felt a little guilty, but then shrugged and thought that I'd try better the next time. I still fall victim to that temptation occasionally, but it's much more rare now than it used to be.

This might have something to do with the fact that if you punish yourself for trying and failing, you stop wanting to try in the first place, as it becomes associated with the negative emotions. Also, accepting and being okay with the occasional failure makes you treat it as a genuine choice where you have agency, not something that you're forced to do against your will.

See also It's okay to be (at least a little) irrational.