What is the command to remove all files but not directories?

What you're trying to do is recursive deletion. For that you need a recursive tool, such as find.

find FOLDER -type f -delete

With bash:

shopt -s globstar  ## Enables recursive globbing
for f in FOLDER/**/*; do [[ -f $f ]] && echo rm -- "$f"; done

Here iterating over the glob expanded filenames, and removing only files.

The above is dry-run, if satisfied with the changes to be made, remove echo for actual removal:

for f in FOLDER/**/*; do [[ -f $f ]] && rm -- "$f"; done

Finally, unset globstar:

shopt -u globstar

---

With zsh, leveraging glob qualifier:

echo -- FOLDER/**/*(.)

(.) is glob qualifier, that limits the glob expansions to just regular files.

The above will just print the file names, for actual removal:

rm -- FOLDER/**/*(.)

If your version of find doesn't support -delete you can use the following to delete every file in the current directory and below.

find . ! -type d -exec rm '{}' \;