FOR YOU.
For your average consumer however, especially considering the brand recognition, the Wii Mini is an extremely attractive proposition if it has Internet. Most of these consumers see the Wii as "the Netflix box". This would've cemented that further in this particular segment.
Or if you want to be creative, price the Wii Mini at $99, remove the optical drive, add HDMI and an SD card slot. That way it's your HD Netflix box and you can connect to the Wii Shop channel to purchase games on your SD card if you want to.
I highly doubt most users associate Nintendo products with media playback (for the moment, TVii may alter things). And now you're talking about doing significantly more work to get the system to support 720p/1080p video output as well as HDMI output when the point of the Wii Mini is to release a stripped down
gaming console to extend the shelf life of an old console being sold at a profit.
Also the original system had an SD card slot, and you would need to rebuild the Wii Shop Channel from the ground up to support digital releases of games. Note we're talking about a system that isn't getting significant developer support anymore. It is completely unreasonable, especially without any form of built in flash memory.
At the height of Wiimania the system had practically zero media playback capabilities, and Nintendo definitely wants to push TVii on the Wii U more than reviving the Wii as a media device.