Effective Parental/Self Control Solutions for Android?

Nothing is truly immutable on these distros from a security perspective in their default version. Only the sealed version of Secureblue has some immutable components, which get cryptographically verified during boot.

Regarding sealed images:

At boot time, the composefs digest in the kernel command line (e.g. composefs.digest=v1-sha512-12:) is verified against the mounted root filesystem. This creates a chain of trust from firmware to userspace, ensuring the system will only boot if the root filesystem matches exactly what was signed.