This is one reason that many band teachers, myself included, chose to start aspiring saxophone players on the clarinet first. The clarinet is basic to all of the other woodwinds, and the discipline required in terms of hand position and embouchure makes them a better saxophone player when they switch after a year of playing clarinet.
The other reason, of course, is that if the band teacher didn't require a year of playing the clarinet first, and then limit the number of students who switched to saxophone, the concert band would have 24 saxophones and 6 clarinets instead of the other way around. In my experience too, the majority of the students who started wanting to play the saxophone, at year's end liked the clarinet enough they wanted to stay with that instrument.