I used to play my Wii on a Sony Wega CRT 32" SDTV using componenet cables for years, up until a month ago.
And the advantages of my LCD would definitly be the super crisp/clearness of Progressive Scan 'of course' when set to 4:3 that is, 16:9 looks pretty crummy in comparison, but you DO get used to it, that's if you want to.
Plus, the color gamut And color gamut options surpass anything my CRT could do....But there's detail crushing in the process depending. 
The only thing i miss about my CRT was the motion handeling, but in return i get superior brightness, progressivescan offering a super crisp/clear and clean image when set to 4:3. Colors so saturated and fantasy-fied colorful that they could LEAP off the screen. raising the Color to 100/max, setting the color gamut to maybe Wide and pushing the Single colors up half way in the Color management options is a MUST for cartoon-based titles.
The LG LK450 1080p LCD is a phemoneal set the Wii, because for none HD consoles in the Wii's Case-orama the input lag is practically none exsistent. 
I just wish the motion and black levels were better for film.........Plus having the color set to 50/100 with everything standard looks washed out, dark and uncolorful compared to my CRT or Plasma.....I have to amp everything up to get it to looks simular OR better but there's detail crushing as the trade off.
I may actually return my set and get a 42" 1080p Panasonic S30 plasma instead.

It's another example of a game that will age PERFECTLY like a galactic rainbow fine-wine.
But again, You do get used to the 16:9 softer visuals and after a while it all starts to look good i guess. But then for the hell of it i always fiddle with the settings and stick it in 4:3 and once again i'm reminded by how inferior 16:9 looks. lol
The Wii Menu is so blurry...