It should technically be possible, but there are licensing issues.
I'm sometimes using Plex to stream from PC to Wii U (in the browser).
It natively supports h264 ("Direct Play") because I can stream 1080p MP4 files without stressing the Plex application on PC. The CPU usage goes to 2-3% with some files that use an audio codec that the Wii U doesn't support natively (like DTS).
I can also stream 4K files, but is stresses the PC CPU by 30-40% because it has to convert it to 1080p.