Finally someone developed this Chrome-like nice feature. I've tried to find extensions like this for months, but today I finally found it.

Thank you! I'm adding this page to bookmarks and I'm also downloading the .xpi file.

Discovered this add-on on the Mozilla Connect community and it works really well. I've tried playing YouTube and BBC and it works perfectly. It doesn't seem to work yet with YouTube Music or Apple Music, but I imagine that will come in time.