How long can you play a note on your saxophone? One measure, four measures?
It depends on which note and the volume. And a baritone sax takes more air than an alto sax.
Being able to play long enough to cover a whole phrase without breathing gives fluidity to the phrase and makes it sound better.
Kenny G holds the record for holding a note, but do you really need to play a note for longer than ten minutes? Who wants to hear that?
Having good posture enables you to hold more air in your lungs. I breath by making my stomach expand out when I play, like a baby does. Herman Riley taught us that a few years back.
And doing long tones as part of your practice routine will get you some control over the notes as well as extending how long you can play.