> There's not a single person (myself included) I have seen use screen time not automatically bypass the limitation instantly as it pops up.
You can take the more drastic approach and lock yourself out of your phone by changing it's unlock code and use a timelock [0] to prevent yourself from bypassing it for a given time. Works also with parental-control like Apps that require you to enter a password/code to unlock. No bypassing here.
[0]: lockmeout.online
The point is that people don't stick with it. Bypassable versions works just as well as this, for a day or two until it becomes slightly annoying. Full lockout will work for a day or two as well, until it becomes annoying. The bypass here is simply that you never use it again.
I think that's extremely dangerous and I would never consider this to be honest. My phone is my only phone, and I need to be able to call emergency services, or answer an important call, at unexpected times.
If I reached the point where I was comfortable literally being unable to use my phone for a period of time, I would just not have a phone or not carry it with me.
You literally can do both without entering your unlock code. That is the whole point, locked phones are pretty useful, but not to kill time.
You can even do more like make outgoing calls using Siri/Google Assistant, Take Photos/videos etc. This is default setting at least on iOS.