Depends on the blur used, right? Straight pixelation is very lossy, but gaussian is less so.
Also I don't understand why the first Mona Lisa results in a picture that when pixelated again, wouldn't produce the original pixelated picture. It is as if the create a face inspirated by the original, but not one that could ever be the original.
You can just as well take these pixels and apply any kind of blur filter - you still wouldn't retain any more information. If you go from say 1k x 1k pixels down to 100 x 100 pixels, you end up with 1% of the original information, no matter what you do.
It's not about turning a shitty image to a nice a clean one. It's about turning a lowres image into a hires version, i.e. you start with 100 x 100 pixels (doesn't matter how you obtained them - could be a section of a much bigger image, for example) and try to extrapolate a 1k x 1k pixel version from it.
The pixelation you see in the examples is just a representation of what little information you have to work with. It's NOT in any way shape or form related to where you get these pixels in from in the first place.
Just to give you a different context here: imagine this upscaling being used to "enhance" a single face in an image like this [1] - there's no way "Gaussian blur" or whatever filter you'd like gets you more information out of that.
In the example image I created, I applied a Gaussian blur to the "pixelated" (i.e. enlarged) version of the marked image section.
As you can see, enlarging the same section using super-sampling (i.e. similar to what you proposed), doesn't change the information content and one version can basically be transformed into the other.