Unvarying unvarying belltone or sine wave sound would be more appropriate for something focused only on melody and not on tone, which is the opposite of OP's point. Sax tone has a lot of variability and control.
The melodic advantages of the saxophone are mechanical, not tonal. For example, to play a scale fragment on saxophone, one need only move fingers, while continuing to blow, creating a smooth, legato sound that can be done very fast. Contrast with guitar, where a note must be fretted and then picked, two separate motions that are difficult to coordinate. Smooth legato playing at high speed is extremely hard. Trumpets have a similar problem, tonguing notes to make changes.
And yes, saxophones have a great deal of tonal expressiveness available, especially once overblowing is brought into play. It's just not pretty tonal expressiveness, compared to other instruments.
Meh. Legato on guitar comes at a cost of expressiveness and note choice. When hammer-on and pull-off are your only ways to sound a note, you lose all the coloration available from dynamics, palm muting, distance from bridge, pick angle, and the million other little things guitarists do to make a note special. And note choice? Scales of any substance will force either difficult position shifts, or legato-breaking string switches.
It can be done, and I certainly do it. But it can't be all that's done, or your sound falls flat.
But it fits poorly into an orchestra. Your tone needs to mesh nicely. There is a reason why the well known classical sax pieces tend to use it as a solo voice (e.g., Pictures at an Exhibition).
And yes, saxophones have a great deal of tonal expressiveness available, especially once overblowing is brought into play. It's just not pretty tonal expressiveness, compared to other instruments.