When I said that the devices are not intended to be shared, I am specifically talking about devices with your Apple ID are not intended to be shared.
Of course the device can be used by multiple people as a payment terminal, but this would not be using someones personal Apple ID. That is the information that you would never want to be sharing. In your specific example of using another iPad to sign people in, that iPad should be using a different Apple ID and the document they use to sign people in would be shared by iCloud to your personal device. That way none of your personal info is on the iPad, but you can still open the document that was used on the iPad and even make changes to it from your iPhone.
For the example of letting your kids use your device, you would absolutely want to set up Screen Time on the device. You could not only use it to limit your notifications, who they can communicate with, the websites they can access, and the apps they can use, but more importantly you would want to prevent them from making any changes to your account by setting it to not allow Account Changes. If they entered the wrong password on that device you would also be locked out of your device as well. Screen Time can be turned on and off on each device without affecting the other one.
For the example of watching a movie on one device without having notifications, but still get them on the other device, you would simply shut off notifications on that device while watching the movie. It will not affect notifications on the other device.
For the example of going for a run, but leave your iPhone at home. Just shut off your phone, since you will not be there to use it and still get the notifications on your watch.
None of the examples provided is justification to share your Apple ID with anyone else. Apple, or anyone else, would never recommend that it is acceptable to share your Apple ID with anyone. In fact, most of the examples provided can be accomplished by not sharing Focus settings and you would set them up independently on each device where you can turn them on/off when you need them. What you are asking for is to allow people to sign in on the device using a guest account similar to the way they could do it on a Desktop or Laptop. iOS is a single user platform and does not allow multiple users like you would see on those other platforms. You are welcome to provide feedback to Apple advocating this approach to using iOS devices.
Product Feedback - Apple