Minor correction on the article: Kunrei-shiki doesn't have a 1-to-1 mapping between kana and letters. You can see that directly in the table they show. Only Nihon-shiki does. Kunrei-shiki is the worst of both worlds.

That's why Nihon-shiki is and will likely always remain the best system for serious students of Japanese - if you even need it at all. But then again, if you're just starting out, the best place to start is usually to immediately start learning kana.