Because of their relative file sizes, downloading audio became fast and easy to do much sooner than video. It created a problem for the music industry pretty abruptly. They didn't have streaming technology (and business structure) ready to go at the time to counter Napster et al. So they went with downloads.

By the time it became easier to pirate video, streaming was further along and the video industry went straight there because it's more friendly to them than the download option.