It looks like it is actually cleaning the cache correctly.
Your template just doesn't seem to output any system messages.
On the frontend, there will be new cache generated directly after the cache has been cleaned, during the same pageload.
So it is correct that the cache folder will not be empty after cleaning the cache via the frontend. But it is new.
You can test this by placing a random file (like an image or whatever) into the cache folder.
It should be gone after loading that frontend url.