The traditional notation system has lasted so long for a reason. It's super difficult to figure out how long notes are meant to last with this notation system. It also takes up a lot more space than normal music notation. Moreover, it looks really difficult to write because of how note durations are represented.
"[The] target user is probably learning easy, contemporary songs, and already knows what they sound like before they learn them."
Leaving out exact note durations is intentional, and probably the main reason why it's so easy to read. The shaded tails from notes just have to evoke what's already in your head.
The problem there is that 90% of people have the lengths of notes in their head wrong. Sure, if you ask them to hum a song, they'll produce something that sounds rhythmically passable, but it's a far cry from being correct.
