For most of today's drummers--even those who play drum solos--the sound of one snare drum in live venues is indistinguishable from the sound of any other snare drum. It's a BANG with snares sound. In recordings, any snare drum will be tweaked by the recording engineer to sound the way the producer wants it to sound. Your $49,000 museum piece snare drum won't sound any better than another person's $49 garage sale snare drum when the sound reinforcement board operator or the record producer takes control. Call me a cynic, and I'll proudly accept the label.
Sorry, but I will have to disagree with some of what you said. The solid maple 5x14 DW Craviotto snare which my son Dan uses for rock gigs has much more definition and a crack and sounds completely different than his Ludwig snares which he uses for jazz gigs and musical theater. The Craviotto is also has a much louder, in your face sound. The DW Craviotto is not well suited for small ensemble acoustical jazz gigs at all. This sound is just all wrong.
For big band work he has a Fibes chrome on fiberglass (the model Buddy Rich used) which has incredible dynamics, projection and response and is very different sounding then his DW or Ludwig snares. When I'm at one of his jazz gigs sitting in the audience I can clearly hear the difference between his Ludwig black beauty or supraphonic which are both noticeably crisper than his wood shelled snare drums. And the Fibes has a very different sound in concert.
And, of course, there are the DW Edge snare drums that make the Craviotto sound tame by comparison. Dan has around a dozen snare drums and all of them get used to compliment a specific style of music or are used depending on the venue. The right snare drum does make a difference.
I will agree that heavily eq'd snare drums will pretty much sound the way the recording engineer wants them to sound in the studio, but playing live is a different story.