I have used my WiiU and Wii browsers before. During the first year of WiiU I mainly used it for DLNA purposes when I didn't have a smartTV, and afterwards for social browsing like youtube, showing off photos, buying online, etc.
It is true that since I've put the HTPC I normally do the social browsing there now, but I do search for game info, youtube (official app sucks) and other media on the WiiU browser from time to time.