The saxophone is the first instrument I chose by myself, after adults had decided for me that I would play the violin and then the piano. So yes, I like it.
But the saxophone has strong limits that makes it more difficult to play than apparently, and difficult to write.
It's always loud. A good musician achieves pp, but not détaché at the low notes. Don't pair it with an alto flute: it belongs with the brass, the piccolo, at least the clarinet or the grand piano.
Some saxophonists sound horrible. Some instruments are worse for that. Sax' instruments had a mellow tone, this held until the 1980s when Selmer introduced the Mark VII that squeaks in forte and was universally copied, alas. Only Yamaha offers presently one model with velvety forte sound, else you must look for historical instruments.
Some notes are brilliant and others are muffled, though the musician and the instrument can improve that. The intonation is far from perfect - again with variations, but far worse than the clarinet and the flute.
The range is very limited. Two octaves and a minor sixth are standard. Coming from the violin (4.5 or 5 octaves) that's extremely narrow. If you transpose for the saxophone, you bump all the time at the limits. The instrument has an altissimo range but it uses to sound plain horrible and any technical sequence is very difficult. Worse, the timbre changes much from the first to the second register, so a composer or arranger has <1.5 octave available. This improves if several instrument sizes complement an other: alto+tenor, etc. But a bassoon, a bass clarinet, a cello or a euphonium are far better in that aspect.
The saxophone uses much air. The soprano less so, the baritone more, but it can't play long phrases like the oboe or the clarinet.