It's hard now to appreciate why Madness were so important at the time - fresh and strong technical musicians when so much of the rock/pop of the era was bland and manufactured. Lee Thompson's honking opening on Night Boat to Cairo (from One Step Beyond 1977) is one of the shortest sax solos - but is still instantly recognisable to anybody who knows Night Boat to Cairo. It always helps a song to be great if the listeners know instantly what's just starting. Just because it's short doesn't mean you can't vote for Night Boat to Cairo as greatest sax solo of all time in the poll.
I never saw Madness live but I have seen a tribute act and was surprised just how much of the typical Madness sound is built on a foundation of Lee Thompson's tenor sax.