It is the obligation of everyone travelling within the area to be able to show a fully valid form of personal identification approved by other Schengen states.[98]
and
Although travellers within the Schengen Area are no longer required to show documents at an internal border (although there have been some controversial instances when they have, and it is fairly common at major land border crossings with Switzerland), the laws of most countries still require them to carry identity documents
Your interpretation of this doesn't seem to be correct. The whole point of Schengen is that you don't have to show ID at internal borders, which were supposed to cease existence. Rather, you have to be able to show your ID at any time whilst travelling ... where "travelling" is such a general concept that it effectively means at all times unless you are e.g. at home.
https://en.wikipedia.org/wiki/Schengen_Area#In-country_check...
It is the obligation of everyone travelling within the area to be able to show a fully valid form of personal identification approved by other Schengen states.[98]
and
Although travellers within the Schengen Area are no longer required to show documents at an internal border (although there have been some controversial instances when they have, and it is fairly common at major land border crossings with Switzerland), the laws of most countries still require them to carry identity documents
Your interpretation of this doesn't seem to be correct. The whole point of Schengen is that you don't have to show ID at internal borders, which were supposed to cease existence. Rather, you have to be able to show your ID at any time whilst travelling ... where "travelling" is such a general concept that it effectively means at all times unless you are e.g. at home.