Yes, I use my mobile web browser to watch video on blogs, forums, YouTube, and other streaming sites on my tablet.
I sometimes visit sites like Soundcloud which has a lot of music to listen to on its website.
I mainly use web browsers to watch video, and listen to music because it is more convenient visiting a website to watch a video, or listen to music than opening up an app, searching for the media file, and waiting for it to open.
I also already have my web browser open on my tablet most of the time.
I also have media stored on my tablet. I sometimes use the built-in video player in UC Browser Mini to open my downloaded video files since UC browser's built-in video player open files pretty quickly, and it is more convenient using the video player in UC Browser instead of opening my downloaded video files with another app which I need to manually launch from the home screen.
I agree, you probably use up most of your bandwidth listening to your music online. Music uses a lot less bandwidth than video, and large image files like high quality animated gifs, so if you have many GBs of bandwidth, you may not use all your bandwidth on music.
My tablet is wi-fi only, so I don't really think of bandwidth usage since I got 125GB of bandwidth per month to use from my internet service provider.
If you are mostly connected to Wi-Fi for the internet, data caps should not be a problem unless your internet provider has limited data caps under 100GB, so you can stream a lot of music on Wi-Fi, and not go over your cap. I think most of the music sites like Soundcloud, Shoutcast internet radio, and LastFM don't use much bandwidth because the Bitrate of the music is lower than regular MP3 files.