Fact: it is possible to build a cornet, today or any other day (time does not change the facts), with all stepped cylindrical tubing, including the bell, that would play in tune and have an excellent cornet sound.
I think some of you are forgetting, or simply don't know, what was going on in the cornet world back in the 1830's. In ca 1830, Jean-Hilaire Asté (aka Halary) invented the cornopean (aka cornet a pistons). The term "cornet a pistons" always leads to some confusion, as players naturally assume it's something like the modern cornet being referred to. But that instrument wouldn't come into being until two decades later.
Lots of old-timers, when they came across cornopeans, referred to them as "old cornets".
Cornopeans have a very good cornet sound. But most of you today have never heard one. They're also around 50% cylindrical vs 50% conical in terms of tubing, meaning they're about the same ratio as the rotary-valved Bb trumpet.
In terms of cornets, if you go back to the early days, and wonder why there were so many different instruments, it's because players were having instrument-builders do personal custom jobs, which created a lot of variation in the instruments. Makers like Courtois often named the horns after the players: the Levy and Arbuckle models come to mind.
Young guys were souping up cornets the way young guys were souping up cars (known as "speeders") in the 1920's and later. The modifications usually had something to do with whatever it was the guy in question was trying to show off: fast tonguing, high-range playing, lyrical playing, really fast playing, speed-jumping in register, you name it.
They were playing circus music, not to put too fine a point on it. Guys like Herbert Clarke were playing in travelling tent shows across Europe and the US. You may have heard of Jenny Lind, aka "the Swedish Nightingale". She was a popular singer in this circuit.
Now, if you think that the cornet sound was restricted to and only known in restricted pockets in the UK, you can forget that notion. The travelling tent shows travelled the world, and were like early television variety shows. Many of the same people played the Vaudeville circuit, which again was highly popular across North America and Europe.
The instruments themselves were like a case of Alexander Graham Bell vs Elisha Grey. The same types of instruments got invented a number of times over in a good many diverse locations. Sax took the valved bugle and re-invented it into the family of modified valved bugles that bear his name- Saxhorns. But the same family of instruments appeared in the US, prior to 1844 (Saxhorn patent date), made by Allan Dodworth, and called Ebor Cornos, or New York Horns. They also appeared in Leipzig, made by Johann Joseph Schneider, who referred to his horns as Flugelhorns. They were also invented, at the same time as Sax, by Vaclav Frantisek Cerveny, whose horns are referred to as Baltic brass.
Without getting into all the instruments referred to as "cornets", suffice it to say that the term "cornet" entails a type of sound, more than it refers to a specific instrument. Ergo, no one can make the claim that a particular instrument has that "classic cornet sound". Nor can anyone ascribe any particular location or nationality to that sound.
The sound Brits refer to as "that classic British cornet sound" was the same sound to be found in US Salvation Army bands.
In fact, much to do with the early Jazz Age in the US was to divest itself of a sound the players thought of as being old-fashioned and out of date. When Louis Armstrong was still playing cornet in Fate Marabel's band touring the Mississippi by river boat in the 1920's, newspaper articles mentioning him at the time often dismissed other players as sounding like "so many Salvation Army cornettists". Herbert Clarke didn't like it one bit when Armstrong took up the trumpet ca 1910, and tried to dismiss Armstrong and the Bb trumpet as "a European fad". His remark is telling, because his mention of Europe gives you some clue as to how widespread awareness of the Bb trumpet was at the time.
Because the cornet pretty much bit the dust in the US by the 1930's, it fell out of memory as well as out of use. There is the false perception in people's minds today that the cornet is a British instrument. Which is complete nonsense. The instrument was just as popular in the US, just as well-known, and sounded just the same as its UK counterpart.
Incidentally- I play a Yamaha Eb, C and Bb cornet. And Eb tenor horn and baritone. Not as dark as Besson equipment, but I prefer the sound because it's brighter. I've always used my old Besson for solos, though.
But an old cornopean or Saxhorn gets just as good a sound. A cornopean maybe better.