I can only speak from my own experience - my teacher put huge emphasis on getting me transposing anything and everything. The aim being to get my transposition to the stage of being able to sight-read anything, regardless of what key the music might be in, or what instrument I might be holding at the time. Brandt was his weapon of choice - he would suggest a number (allegedly at random) and then pick a transposition (so it could be "4, in Eb", "7 in F", "31 in A" - for example). He also had a number of other books we used, either with me having my own copy, or he would bring his books out, to make sure I hadn't been learning them in secret
I would love to say he succeeded, but that would be, unfortunately, not the case - this is entirely down to my not practising this skill enough anymore, rather than anything lacking in his teaching.
It has, I admit, always puzzled me - the quasi-obsession with learning every excerpt in the standard repertoire. Yes, it is great to know how they go, but being able to read anything new that might come along is, I think, as important, if not more so.
Speaking to some of the big-name players over here, they teach the standard orchestral repertoire, but also make a big point of getting people to sight read. The standard amount of rehearsal for a concert is so limited that your sight-reading needs to be practically flawless - it is quite common to do even a difficult contemporary piece on only one or two rehearsals, potentially without having seen the music beforehand (in some cases, it might not have been written until the first rehearsal - then you get revised parts for the second rehearsal!!).
Thinking of the different schools of playing - I am very interested in your views regarding which trumpet to use. Over here, the Bb is pretty much the standard for everything. Over in the US, the C trumpet is dominant. I have read a number of posts saying that if someone were to even turn up to auditions (even for college orchestras) and play on a Bb, they wouldn't be considered. To me, it is what comes out of the end of the bell that matters, rather than what type of bell it is. If someone plays a Bb and sounds great, they would get the seat. Is this just a UK (or even just a me) attitude?