Well, not ALL.
Phil Woods was a very fine clarinetist. Lew Tabackin is a fine flutist. Sonny Stitt played both tenor and alto at the very highest level, and with somewhat different concepts. Benny Carter played both alto and trumpet. Sidney Bechet played soprano and clarinet. John Handy - tenor and alto. Coltrane - tenor and soprano. Dolphy - Alto, bass clarinet, flute. Harry Carney - baritone, alto, clarinet, bass clarinet. James Moody - alto, tenor, flute. Yusef Lateef - flute, oboe, tenor. Rahsaan Roland Kirk - flute, soprano, alto, tenor. Tom Scott plays pretty much all the woodwinds. Paquito D'Rivera - alto and clarinet.
There are advantages to picking one and sticking with it, but there are advantages to doing it the other way too.