That's right, it replaces the pen and paper sleep logs, which rely on self-report. There was a period where I was using the app at the same time I was tracking my sleep on a fitbit, and they were quite different. But the point of sleep logs isn't to be accurate, but to capture an estimate that will change over time (hopefully). I have used CBT-i on myself and found it hugely useful, despite the limits of self-report sleep logs.
A benefit of the app is it automizes the averages of time in bed and time asleep, but I think its main benefit is that people have gotten used to having a phone on them at all times and are more likely to remember to use the app to track sleep. So it might just improve adherence. With older folks or people less familiar, I would still provide or encourage pen and paper.