You can set down times for the whole phone and lock it remotely which is of huge benefit for bedtimes!
I don't want (yet, but it will come) for them to have their own device that I control as you explained.
Android may have alternate launchers you can install (they are just apps) which you can customize how you need. One of the best features of Android imho.
I tried helping a friend with their kids Amazon tablet and left the experience wanting to wipe it clean and just define what 4 buttons parents can put on the screen.
Other tech:
Apple has a guided access feature which locks it to one app (except it's handed to them).
We're holding off on personal screens for now until the information diet can be tamed and managed. Looking for a smartwatch with a phone with physical buttons and no screen. Seem to be some options.
i don't think multiple account is an /e/OS feature, but must be coming from lineage/ASOP so other ROMs should have it too (unless it was intentionally removed)