just a few vaguely related thoughts..
the soprano sax was in danger of becoming extinct at one point - Steve Lacy said they when he switched from clarinet to sop sax in the 1950's there was no one else in New York whom he could talk to or consult about playing the instrument. Sideny Bechet had moved to Paris by then.
It appears that none of the american sax manufacturers had updated the designs of their sopranos since the late 20's and it's possible that they didn't make many sopranos post WWII except as special orders. Given that Selmer did update their soprano design we can assume that demand was greater in Europe.
Opinions vary as to how John Coltrane got into playing soprano sax, but he must've heard Steve Lacy at some point. Although Lacy's role is crucial, I think it would be reasonable to suggest that Coltrane is the one responsible for the popularity of the soprano sax in jazz and it's probably his playing and tone that have had the greatest influence. And it's Coltrane's tone that has sometimes been likened to an indian
shehnai or oboe. 'Trane was certainly interested in indian music, but we don't know if he was consciously copying the great indian shehnai players like Ustad Bismillah Khan or whether he just naturally sounded that way..
It could be argued that Coltrane's soprano tone is an extension of his tenor tone, as anyone who's accidentally played one of his albums on tenor at 45rpm may have observed. There's also the fact that he was having to play really loud in order to make himself heard over Elvin Jones's thunderous drumming in an era when PA systems were rudimentary or non existent.
In the 70's the rise of jazz fusion and loud electric bands made it necessary to go for louder, brighter sounding mouthpieces in order to hear yourself above the din and the resulting tones were sometimes a bit thin, bright and squealing....
and of course there was Jan Garbarek and that haunting Berg Larsen tone as well as other great soprano innovators like Evan Parker, Roscoe Mitchell, Lol Coxhill, Charlie Mariano and the almighty Wayne Shorter all of whom have a little bit of Coltrane in their playing. Zoot Sims is one of the few who broke the trend and got a full rich tone out of the instrument, Johnny Hodges should also get a mention..
So the thin, buzzy, reedy, hollow, "oboe" tone is part of the history of the instrument.
I tend to think that the soprano sax torments you with the tone it thinks you deserve rather than the tone you think you want