Well, this is of course the result of an evolution and what NOW is the situation... but it wasn’t always like that.
At the time when Sax made his first saxophones things were very different, it wasn’t him to chose for Eb and Bb , it was the players (so it was the market).
“..Since the first saxophone was invented by the Belgian instrument maker Adolphe Sax in the early 1840s,[4] saxophones have been produced in a variety of series distinguished by transpositions within instrument sets and tuning standard. Sax patented the saxophone on 28 June 1846, in two groups of seven instruments each. Each series consisted of instruments ranked by pitch, in alternating transposition. The series pitched in B♭ and E♭ soon became dominant and most saxophones encountered today are from this series. Instruments from the series pitched in C and F never gained a foothold and constituted only a small percentage of instruments made by Sax...”
Aside the instruments in F were also instruments in C and G which never really (with the temporary exception of the C-melody tenor and C soprano) took a foothold .
You have to remember that Clarinets formed the inspiration for the saxophone, Sax wanted to make an instrument, predominately, to replace clarinets ( for volume and ease of playing) in military marching bands where clarinets where overwhelmed by brass instruments. Clarinets, up to that point had been produced in almost any key so that the player, would switch clarinet rather than playing in more complex ways.
The fact that the saxophone were first introcuced in the military bands favoured the remaining of the pitches ( Bb and Eb) which were shared by most brass instruments present in those bands too , that is why only the instruments pitched in those keys are left (practically) nowadays, but, again, itwasn’t like that when it started.
“....Sax created an instrument with a single-reed mouthpiece and conical brass body. Having constructed saxophones in several sizes in the early 1840s, Sax applied for, and received, a 15-year patent for the instrument on 28 June 1846.[16] The patent encompassed 14 versions of the fundamental design, split into two categories of seven instruments each, and ranging from sopranino to contrabass. A limited number of instruments in the series pitched in F and C were produced by Sax, but the series pitched in E♭ and B♭ quickly became the standard. All the instruments were given an initial written range from the B below the treble staff to the E♭ one half-step below the third ledger line above staff, giving each saxophone a range of two and a half octaves. Sax's patent expired in 1866.[17] Thereafter, numerous other instrument manufacturers implemented their own improvements to the design and keywork.
Sax's original keywork, which was based on the Triebert system 3 oboe for the left hand and the Boehm clarinet for the right, was simplistic and made certain legato passages and wide intervals extremely difficult to finger; that system would later evolve with extra keys, linkage mechanisms, and alternate fingerings to make some intervals less difficult...."