Most people might disagree but after running all 3 on HDTVs for a decade+ (I have legit component cables for all 3 including GC) I’ve come to the conclusion that they look best in 480i on a regular consumer level CRT TV.
PS2 is native 480i in many ways – most games do not even generate any sort of progressive image, and those that do usually do so with compromises, so that’s an easy one to say run it on a CRT.
Xbox and GameCube do generate 480p framebuffers before outputting 480i but most games are designed around CRT TVs, from things like UI being meant for 4:3, to art assets looking better with some fine detail left to imagination, to even considering the a 720x480 image as something intended to be band limited by low TVL consumer CRTs with nice softening filters giving an anti-aliasing-like result. I wrote out a bit of a comparison last year of a best case scenario of 480p CRT vs 480i CRT and meant to make a better argument but yeah take it for what it is.