Why transpositional instruments?

[Scaper]

I understand when we play a C on the Alto sax it's an Eb on the piano,
but why are sax's designed this way? Is there some advantage to this?
Sure seems inconvenient to me.

[Bill Mecca]

Sax designed it that way so you could play other instruments in the family with the same fingerings

i.e. LH 1 is B on sopranino thru contrabass, LH1+2 is A and on and on. The fingerings are the same, other wise to play alto and tenor you would need to learn two seperate sets of fingerings.

[Paul Coats]

The instruments of the sax, clarinet, and saxhorn family (cornet, alto horn, baritone horn, tuba, etc) overlap in their ranges in such a way that it makes for easier arranging of the voices without putting any one instrument at the extreme of its range.

There were two basic families of saxes planned by A. Sax. One was the orchestral family, those in C and F: F sopranino, C soprano, F mezzosoprano (a little smaller than the Eb alto), C tenor (more commonly called the "C Melody Sax"), F baritone (never made), and C bass. The C bass was the very first saxophone, followed by the C soprano.

The other family was the military band family, pitched in Bb and Eb: Eb sopranino, Bb soprano, Eb alto, Bb tenor, Eb baritone, Bb bass, and Eb contrabass.

Between these two familys, the Bb-Eb family of instruments generally have a deeper, richer tone, for practically the same range. They were more comparable to the common Bb instruments already in use in military bands, the Bb clarinet and Bb trumpet, etc. The saxophone was accepted into the bands as standard instruments much sooner than the orchestra, where it is still an "on call" instrument, for the occasional performances of Bolero, Pictures At An Exhibition, An American In Paris, etc.

BTW, Adolf Sax also designed what is now the modern Bass Clarinet and improved many other instruments.