I have eczema, and at one point it got so severe from taking (too-)hot showers, that I could hardly sleep for weeks because of the discomfort. Out of desperation I gave up showering altogether so that I could heal. I eventually realized that I didn't really smell. After my skin healed I didn't resume showering. That was about four years ago. I've never had anyone (including my partner whom I live with) tell me I smell under normal circumstances (in fact I asked my partner directly), nor that my skin looks or feels oily or abnormal in any way. Same with my hair. I do smell for a few hours right after vigorous exercise or something, but it's nothing a little deodorant and a fresh shirt can't fix.
I don't know if everybody is this way - I'm sure it varies a lot by body chemistry - but for me at least there have been no downsides. In addition to saving time, I have to think I've saved an enormous amount of water. From the article, it sounds like I may be healthier for it too.