[ . . . ] And maybe that's it? If John Coltrane or Sonny Rollins had chosen to play Martins, would our horns be worth a lot more money now?
Yes. Especially Coletrane. If you were a younger player getting into jazz, you might not look any farther than what he was playing. If Coletrane played Martins, that company might still be in business!!
Celebrity endorsements, or just accidental association, can really light a fire under sales. The only reason the Rickenbacker guitar company is still in business is probably because John Lennon happened to pick one up in Hamburg, Germany, even before the Beatles got big in England. After they got big, other bands (like The Byrds, The Who, Etc Etc) started playing Ricks, too. The company was never a giant in terms of sales (they were always on the expensive side), but they've still got a persistent niche market. Same goes for the Vox amplifier company - it's what they Beatles played!! They're still around. Even that Hohner bass guitar, with the faux - bass fiddle body, that Paul played in the early days is still being made.
Does anybody consider the endorsement issue? Selmer was just better at getting their horns into the hands of more name players - and their horns were as good as any others, and better than most new horns in the 50s and 60s. There may have been peer pressure working in their favor as well, especially in New York, where an up and coming player really needed to stay with the crowd to rise to the top of it.
I once knew an old guy who was a young session player in New York starting about the mid '50s. He had a new Martin alto, and he preferred it to Selmer's horns. He said that he quickly learned from other players that the fact he wasn't playing a Selmer could hurt his ability to get work. The interesting thing was that this was partly on account of the Selmer players themselves, but also because that for whatever reason a number of the major producers for the various kinds of studio work he was pursuing had decided the only horn serious saxophonists played were Selmers, and they would actually ask what you were playing as a quick and dirty rule-of-thumb for new faces. He said he found it all ridiculous, but he didn't want to risk losing work so he got a Mark VI.