I'm thinking more and more of doing that, but prompted by the fact that the phone is a second-factor authenticator for so many things. I really don't want to lose that phone. I should just leave it home and carry another one just for urgent stuff.

I've thought about doing that, but it seems to require multiple Google accounts - one for the "child" and one for the "parent", which is hard to achieve without also having multiple SIM cards with different phone numbers that can be used for the account registration. I assume the process is designed to be full of friction to prevent people from freeing themselves of the addiction.

You don't need multiple SIM cards; you can just create new Google accounts. I have my main google account set as the child of a different account and it works great. But the set up was somewhat annoying, took me a couple hours.

I've been postponing writing a guide on how to set this up for a while, but I think I'm motivated to do it now, I'll try to have something up by the 8th here https://tim2othy.github.io/ws/screen-time/, maybe useful for you.