Well, the obvious reason is that pictures with the shadows lifted one stop look hideous. Another reason not to lift the shadows is that there is nothing wrong with them, and there need not be because there is no reason to accept your arbitrary condition that the exposure is set by the highlights.
Of course, you are perfectly entitled to disagree about the hideousness of lifted shadows, or the sacredness of highlights, but you are still basing your claim about the usefulness of knowing capture DR on an aesthetic judgement about the final image, which you previously said you weren't.
It is distracting to always mix up aesthetic discussions with technical ones.
I did not talk about pleasingness. I did not say that the shadows have to be lifted in order to get a pleasing image.
The shadows have to be lifted to display the information at 11 stops below the highlight point because that was the brief for the image. By not displaying them on the output, you are not fulfilling the brief. The image can have pure documentation purposes and does not have to have any artistic value at all. Saying that the output medium only has 10 stops of dynamic range is no excuse for hiding the information that was supposed to be displayed.
Likewise for the highlights, the brief was that they cannot be clipped, and therefore they set the maximum exposure that can be set.
These are the conditions of my example. It is no use arguing the conditions, they were not up for debate.
The question is, how do you solve this photographic situation? It is a common one, e.g. when photographing interiors with windows.*
Another way to fullfill the brief is to light the dark parts of the image, or to do multiple exposures etc. But if for some reason you are forced to use one exposure and no additional lighting, then the example applies.
I know that lifting shadows too much can lead to unpleasing results, but that is subjective, and I'm not going to impose my subjective criteria on other people. But the point is that the information is there on the 14 stop DR capture, while it is totally buried in the noise in the 10 stop DR capture, and cannot be recovered with any kind of processing. This proves that capture DR that exceeds the output DR is useful.
* I have seen plenty of interior architectural photography with large dynamic range printed on paper, which has a much lower dynamic range. It can be done.