I think it Depends. . .
I think it depends on what kind of music you are playing. Obviously in jazz, you see a lot of guys playing tenor and soprano. And, of course, they have the advantage of being in the same key.
In rock and blues, it seems to be more tenor/bari, tenor/alto, or tenor/flute. And, of course alto/bari. I remember seeing Roomful of Blues last year. The three piece horn section had two saxes in it. One guy was playing tenor and alto. The other guy was playing tenor and bari.
I play tenor and bari for the most part (more of a blues/rock/r&B guy.) It would certainly make life easier to play alto and bari. But I just really don't dig playing alto that much. I have an alto to take on trips with me to give me something to practice. But I don't reach for it very often other than that.
The different keys are less of a big deal in blues/rock/R&B stuff, because there really aren't too many heads to learn. And they are pretty simple.
One thing is that if you play an Eb sax and a Bb and play both rock and jazz, you really do end up playing in every key.
The more interesting challenge/problem with me comes with jazz stuff. I'm in a rehersal group playing tenor, which is my preferred horn. But when I go to a jazz jam, I tend to take the bari. The jazz jam I go to is full of tenor and alto players -- many of them very good. I'm the only one who shows with a bari.
Interstingly, I have heard a number of guys where I thought their alto/bari or tenor/bari play sounded pretty good. Not so many where I dug both their alto and tenor playing. This seems to be particularly true of alto players who try to pick up tenor once in a while.
I'm not that good at memorizing heads. And the Eb/Bb thing just compounds the problem.