Distilled water is always an option for brewing. Adding important major and minor ions that help promote good mashing performance and fermentation performance is a good idea too. Even though brewers in Pilsen were able to brew great Pils using water with really low calcium, we now know that calcium is very important to good mash and yeast performance.
If starting with distilled water, adding gypsum and or calcium chloride to boost the calcium concentration to at least 50 ppm is a good idea. I'm not sure where the notion that sodium is necessary came from, but its not needed except as desirable for flavor impacts. I'm with Jeff regarding the mention of the Beersmith article. Although I appreciate their software, I'd say it was safe to say that brewers should not get water knowledge or advice there. Kai's and Palmer's sites are much better for basic water information.
Distilled water will work OK for light colored beers, but might produce a lower mash pH and thinner, lower bodied beer as the color increases. Alkalinity is a necessary evil for brewing darker beers. Adding alkalinity is a little tougher and that may be a reason why a brewer might want to include some of their tap water in their brewing water. These are nuances that cannot be covered in a quick message. But as a brewer increases their brewing knowledge, those nuances become more understandable and approachable.
Understanding what you need for brewing great beer might not be a goal yet, but brewing a good beer is probably a minimum goal for any brewer. Adding minerals may not necessaryily improve efficiency, but it might make better tasting beer. Keep doing what your doing and add knowledge with each brew.