Doppler's support for iCloud drive is limited.
You can store files in iCloud Drive but there's no way to stream them (i.e. play the file as it downloads). That means if you wanted to play a file that isn't downloaded, Doppler would need to download the entire file before it can be played. Depending on your internet connection and the size of the file, this could take a while.
In addition, iOS periodically removes downloaded files to save space. This means a song you downloaded might not be available later and you would need to download it all again.
iCloud Drive was designed for documents — not for general use in apps like Doppler. If Apple improves iCloud Drive, Doppler will try to support it in the future.