You'll see no improvement switching from component to RGB on the Wii for GameCube games on an HDTV, unless your TV handles interlaced component signals poorly, and for some reason, upscales better via RGB input (which it may do as RGB are SD signals, so it's logical the TV might upscale that input).
All this comes down to is how well your HDTV handles upscaling SD signals, some are OK, others are terrible. As most GameCube games are in 4:3 I'd find a 14-21" flat CRT TV and set a Wii/GC up somewhere else with an RGB cable if you don't want it to look too bad, but fortunately my HDTV handles SD very well. 240p is completely strawberry floated though so I use a PVM for that and N64 - PS games are all handled well via backwards compatible PS3. So I'd do that or get an HDTV that handles SD better, or find an input that is handled better (it may well be RGB SCART).
Also bear in mind only some RGB cables for GC are actually good.
https://www.retrogamingcables.co.uk/nin ... le-dol-013Generally speaking, any SD signal blown up to 32/37"+ is going to look like a blurry mess by today's standards, no matter how you sugar coat it - unless it's being rendered in 2:1, 4:1 etc. in a 1080p emulator like Wii U (where must the games' brightness is strawberry floated) i.e. you're getting clean square renditions of pixels. Then it just looks something like Shovel Knight. Super Metroid on Wii U is a pretty good example as that game isn't ruined (although it's "optimise" 50Hz, plays well for me).