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Why did the clarinet and trumpet get made to 'be' in B♭? Could they have been made to produce concert pitch C?
This would make a composer's life so much easier when physically writing scores. Surely a slightly longer instrument wouldn't make that much difference to sound, timbre, etc?
This goes back to the early days of "modern" instruments. Initially, instrument-makers did not have the accuracy of instruments (mechanical) to create keys, accurate boring, etc. If you look through the history of any wind instrument, you'll see such profound comments as "and then it received two keys!" Because most instruments were created at a time before using keys, you had an instrument in a single scale degree. If you had a C clarinet, you could not play F#s or Ebs. You played diatonically, in the C scale.
As instrument-makers learned more precise tools and were able to create more complex systems, the number of clarinets needed to play the full range of scales diminished. We were left with three soprano clarinets: A, Bb and C. Bb sounds the best, and was determined to be the winner of the clarinet races. It is most commonly played. However, any professional clarinetist has all three "orchestra clarinets", because there are parts still written for them.
Part of the problems with the other instruments: the modern A clarinet has been designed to fit the Bb mouthpiece. Unsurprisingly, this is a less than perfect match. It means that the A clarinet has interesting intonation problems and what's commonly referred to as "the grunt" -- a sort-of grumbling sound from the instrument in the second half of the clarion register. It just doesn't want to play them!
The modern C clarinet on the other hand tends to be a bit brighter (is smaller) and also has different intonation problems than the standard Bb. I think the C instruments are not bad, but because they aren't standard, harder to find essentials like reeds, ligatures, replacement parts, etc. Not hard, just harder.
These instruments are only commonly used today in orchestra. In bands of any variety, the Bb is commonly used. It's not a difficult transposition, and trying to "re-write" for concert pitch would probably induce screams as loud as asking a violist to play in treble clef. :-P
The long and short of it is: there are more than one clarinet, there are reasons for playing any, and those reasons probably have more to do with tradition than anything else.
Originally there were 3 clarinets: A, B♭ and C
According to Wikipedia, the C clarinet — being the highest and therefore brightest of the three — fell out of favour as the other two clarinets could cover its range and their sound was considered better.
Building to make the composer's life easier wasn't one of the design requirements, and in fact isn't for most instruments!
The point is not that people specifically want instruments with a natural scale other than C. The point is to make different sizes of the same instrument and have them all playable with the same fingering without additional learning effort. And different sizes will result in instruments starting their scale on different notes (unless you make them so big that it's exactly an octave above or below).
But to take advantage of the reduced learning effort, at least one variant has to be notated in a transposing manner. And if composers, conductors and copyists have to deal with transposing instruments anyway, it's a better idea to build your instrument variants on those scales that work especially well for that particular shape and have both variants transposing, raher than have a "standard" C version and e.g. a non-standard A version.
(And what does it mean that a specific scale works "better" for an instrument? Well, the difference between an A clarinet and a B clarinet is subtle, but clarinet players will tell you at length that it's very characteristic, and the C clarinet is another thing altogther.)
As for the trumpet, the choice of key Bb goes back into history. I have no sources available, but has been told that it goes like this.
The valved brass instruments started to come inte play a bit into the 19-th century. At that time the large buyers of instruments were military bands in continental Europe. The military had large marching orchestras and liked the sheer volume of brass instruments. The military ordered full sets of instruments, from large tubas up to small trumpets and anything between. From some reason they decided to select the Bb key and standardize on that. Exactly why, I have no idea of.
From this start, the market started to contain a lot of Bb brass instruments and players. The production turned inte a mechanized industry. The Bb instruments probably were both better and cheaper than the alternatives, so it spread outside of the military to other areas.
From a player perspective, you like to play the same key instrument as your teacher and that you started playing on. From a composer perspective, it does not really matter -- learning to write for transposing instrument is learned from the very beginning and is not really complicated. So the tradition of Bb keyed brass instruments has stayed with us.
(It should be noted that the Eb keyed instruments fit in the middle between two octaves of Bb and fits well into how to transpose).
