I have been trying to play traditional music (mostly Scottish) on the C melody sax lately. Key is not a problem (it fingers like a conventional flute) but it isn't very responsive, particularly when the tune has wide leaps - it feels like you have to spit each note individually down the instrument. A recorder, flute or clarinet does fast stuff much more easily.

Maybe a really expensive sax might be better, mine is a Buescher from the 1920s.