"Puritanical" is definitely meant to imply unhealthy, which is why it's got such a negative connotation. I think even in your example, you substitute "wasted" productivity (in the sense of going beyond contractual obligations) with other productivity, albeit towards another direction. I think that's what the parent's post is pointing out: this obsession/compulsion with filling in all time with productivity. Why can't time just be "wasted"?