Doesn't Duolingo allow you to switch off the romaji? Of course even with that, you are still inputting romaji from yoru keyboard to get the kana to show up onscreen. That in mind, you could buy a Japanese keyboard and turn on "kana" mode, meaning you would use the kana symbols on the keys to type. No one in Japan uses that mode — everyone just types in romaji. But for language learners, there is some advantage to using kana input. You'd need a JIS keyboard though.

I think Duolingo embraces the exposure theory, the idea that the best way of learning is to just repeated expose yourself to sentences and build up a familiarity to it, not unlike a child learning their native language. It's a linguistically sound theory and works well for many people, but it can be frustrating to people who want the guidance of the grammar to help them.