The idea is to let parents decide which apps are suitable for their child, for each child. Password-gating app installation (just like sudo on Linux) is not only easier to implement and use, but also much more flexible and powerful than a fixed age-based rating system.

It also prevents the legitimization of app store monopolies because no centralized authority is needed to create or enforce a rating system. And there will always be apps that don't comply with a rating system out of privacy concerns (it leaks the user's age, which is just an extra data point to track you with), and then they'll eventually try to ban non-compliant apps from running on the device completely. That's what enforcing an age-based standard would take. And even then it would still not fulfill its (claimed) purpose that well.

Principle-wise, parenting should be the responsibility of parents, not governments or corporations. Those large organizations have their own agendas which are somewhat misaligned with the individual human being.