As far as I know there are no modern songs that come up as etudes or fantasias.
If you know your math, modern songs are products from the 20th and 21st centuries, while most etudes that are now used as a part of a method are made from the 17th to the 19th centuries.
Oh, unless you think Mozart travelled back in time or Chopin travelled in time and used "No Other Love" on his etude.
No I don't think he did.
EDIT: As you expounded your question, I became confused the more.
But anyhow, now I get you. The question should have been similar to "Do you know any piano etude/fantasy based on a classical piece?" and in the details "Like Marc-Andre Hamelin or Arcadi Volodos with their transciptions."
Here are most famous I know
1. Leopold Godowsky. Of course who could forget his etudes on Chopin Etudes. My favorite is not included in that set though. My favorite is his transcription of Saint-Saëns's The Swan, only lasting about less than two minutes.
2. Georges Cziffra. I think you know that pianist who insisted that Liszt's Hungarian Rhapsody no. 19 be changed, proving his egocentricity with history, which still does not prove right. But you can't deny that he did some pretty difficult music that no human (average) could comprehend. Like his Khachaturian Sabre Dance transcription. Flight of the Bumblebee (which is terrifyingly difficult, even only with Rachmaninov's transcription). They're mostly played by Yuja Wang.
There are also great improvisers on the piano -- some unheard of in YouTube or somewhere in the Arctic region.
Sorry -- my head is aching and only those mentioned are all I could think of.