This was a big thing in the medical imaging community (where I did my stint as a CV researcher), folks were hallucinating microscope images and CT scans with no information theory justification as to why it worked.
Super resolution IS possible, but it must be done by synthesizing new pieces of information, not by inferring based on what other similar looking objects looked like. A cool technique by my former advisor does this with microscopes [1].
Deep learning has a place here, just not as a "lets create information" step, but as a way to learn how to synthesize additional information about images from more sources (i.e. more similar to how Google does Night Sight [2]).
Edit: if you want to see (an attempt) at using deep learning in this field you can checkout one of my papers [3].
[1]: https://en.wikipedia.org/wiki/Fourier_ptychography [2]: http://graphics.stanford.edu/papers/night-sight-sigasia19/ni... [3]: https://openaccess.thecvf.com/content/ICCV2021/html/Cooke_Ph...