At the time of its release, the Wii was competing with Microsoft's Xbox 360 and Sony's PlayStation 3. The latter two touted a graphical output of 720p, which could be upscaled to 1080p on the right display.
And as for the Wii? 480i with the included composite cable.
This was a revelation that many could gamers could not abide, and left the Wii behind for its beefier competitors -- even if they had previously identified as Nintendo fans.
Yeah, 480i may not look the best on a 52" 4k display, but I've always felt that placing too much emphasis on graphics leaves behind the other factors that make a game great, such as responsiveness and fun factor, which the Wii has in spades -- and if graphical output is all that's holding you back, there are plenty of component cables or Wii2HDMI adapters can bump it up to 1080p.