Your daughter might be partially right in that it is possible that due to high dioptre (I would say >6.0 is high), you will see a phenomenon called "facial displacement":
https://www.2020mag.com/article/avoiding-facial-displacement
The website states:
Today’s lighter weight, higher index materials coupled with our ability to produce aspheric, digital lenses have eased some of the problems of using large lenses. Yet neither selecting a different material nor using aspheric curvatures can correct the issue of facial displacement, which is primarily a problem for prescriptions in excess of about 6 diopters.
Also seen from this image, if you want a physical description of what is happening:
![concave lens effect on how the face looks](https://i.sstatic.net/QSWcsNxn.jpg)
From your description it seems that the displacement is "facial inset":
The best ways to reduce facial inset are to control the amount of lateral prism at the outer edge of the lens, and to reduce the distance from the back of the lens to the patient’s face. On strong minus lenses, you may achieve a somewhat better result by having the lab roll and polish the lens edges. This will also improve the appearance of the thick lateral edge of the lens.
Unfortunately there is nothing that physics can do. A good optometrist should be able to better shape plastic lenses (additionally benefiting from being lighter for high dioptres), but I don't wear glasses so I don't know if this is something that will result in more expensive prescription spectacles.
While not entirely unavoidable, it is possible that plastic lenses can be more comfortable, but the fact of the matter is that regardless of the optical material, facial displacement will occur at high dioptres.