I'll venture out on a limb here and say that there are "custom" saxophones...the businesses themselves just do not operate under the same model as the custom brass/guitar/violin makers. Steve Goodson would call his horns "custom" (and I think most would agree) even though I doubt he personally hand hammers the tubing on all his instruments. I would imagine the problem lies in the complexity of parts with the saxophone. I think there is a good reason why the trumpet and trombone family preceded the saxophone family by centuries...they are easier to make by hand. Saxophones have so many small detailed parts that machines do the job better than bare hands. "Custom" horns like Goodson's come from parts bought from other manufacturers and it is the customizers job to improve upon that.
Another thought: I think in the world of saxophones, the hand-made customization is all about the tech. Whereas custom stringed instruments bear the name of its craftsman, I think there is a sense of players choosing their tech as they would choose a new horn. Many professional horns bear the name of its respective tech....i.e. an Emilio rebuilt VI, or a Curt Altarac rebuilt New Aristocrat, etc. A good tech can improve upon the factory and create a new instrument bearing the unique traits of their artistic taste. There is a reason that an overhaul is close in price to a new horn
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Another thought: I think in the world of saxophones, the hand-made customization is all about the tech. Whereas custom stringed instruments bear the name of its craftsman, I think there is a sense of players choosing their tech as they would choose a new horn. Many professional horns bear the name of its respective tech....i.e. an Emilio rebuilt VI, or a Curt Altarac rebuilt New Aristocrat, etc. A good tech can improve upon the factory and create a new instrument bearing the unique traits of their artistic taste. There is a reason that an overhaul is close in price to a new horn