I wholly agree that code comments can be greatly reduced by better code, most notably with code that has well-named variables and methods as well as through reduced complexity through refactoring.

However, I think the way the OP title is phrased, "Don't Comment" makes too strong of a statement against comments, when I think the better, albeit softer statement would be: "Write Better Code and Fewer Comments"

The main argument against commenting period is that comments are inherently not part of the workflow/compilation process, so it takes an extra level of cognitive awareness and maintenance to make sure they stay up to date with the specs. Other than that (very big) hitch, there's nothing inherently wrong with comments...except that in practice, a huge number of them indicate a code smell, as well as being a maintenance liability.

This may have been outside of the OP's scope, but I think it's worth mentioning that well-written and copious tests can also serve the function of comments...unlike comments, they do break when the code they document is changed, and so thus they're easier to maintain in that you can't go forward without fixing them (which introduces its own maintenance chore, and so on and so on).