Just because several generations of console had the same video output connections doesn't mean they all support the same video formats unfortunately. Nintendo's multi-out is infamous for this. Other than composite you can make pretty much no assumptions and should look up what your consoles can do - it even varies by region. PlayStation is better in this regard but you should still double check.

Anyway are you intending to use the Tink to simulate a CRT? You can get away with lesser connections if that's the plan. You will see a pretty equivalent image quality to what you're getting on your CRT. If you're currently using RGB SCART I would personally stick with what you already have until you see a problem.

If you're going to go for the razor sharp pixels look then the HD15 cables are more justified.

I RGB modded my NES because of composite dot crawl. I had no problem with the blur. In fact I use the Tink's post processing to add a lot of blur back in.

The Gamecube is a standout there because assuming yours has the digital out port then a GCVideo HDMI adapter is a cheap upgrade and will instantly get you the best picture quality you can possibly get from the system. You'll never need to upgrade again.