The relentless 'You must play your major, minor scales and arpeggios!' 'you must play your Giuliani right hand exercises!' banged on and on by the music teachers employed by conservatories and music schools for the required technical exams cover the fundamentals of the 'virtuosic' repertoire and I really think regularly practising technical work makes learning new pieces a much quicker process. The musician can see where there are rapid runs, broken chords spanning several octaves and be able to efficiently execute them based on experience playing these types of things out of context.
I do wonder why it is that by far the technical work that is advocated by these establishments have their roots in the 19th century ideals of the virtuoso and are very particular to that repertoire. Personally I have found myself having to write my own technical exercises to learn music by Carter, Andriessen, Henze and others in order to be as efficient in my learning of these works as I am with the works of Giuliani, Legnani and Mertz. There is certainly a sizeable repertoire of music being played by students for which 19th century scale and exercise books are barely appropriate, yet there is only one standard set of technical work for each instrument that I have ever come across in music schools' curriculum.
Are technical exams akin to standardised testing now, or what? Is this just a futile attempt at saying 'one size fits all'?
The scales, arpeggios routines are standard, and they are fundamental. You are completely correct in that they in no way specifically address any other configurations, let alone those found in modern and contemporary music that are that much different from what is found in the common practice rep.
Those basics are something everyone in a university or conservatory who is majoring / minoring in instrumental performance (and any sort of music major must minor in an instrument, the last I checked) are expected to have well under their belt. I do question testing them each semester once the student has 'proven' their self, though.
I was a bit stunned to learn that even those in the advanced high-school level music programs in the U.K. and your neck of the woods were expected to have scales 'up to four accidentals,' ('only four -- why not all of them?) and if that is what unis and conservatories there are looking at for their entry level performance students, then perhaps there is still a need for those fundamentals being tested. In my (long-ago past) experience, knowing them all in both theory and instrumental practice was an entry-level uni / conservatory requirement.
The basics are a decent 'warm up' for about any musician, while 'basic' and 'warm up' are completely relative. I know pianists who warm up starting 'cold' by going straight into, say, a Chopin Etude at tempo.
Teachers I have had, from middle school on, have all advocated that the best technical exercises are the ones you extract from the repertoire you are working on. Difficulty with executing any part of a piece means isolating it, and playing it directly as an exercise; with enough experience, the player can then think up other exercises based on the particular problem as well. For us two-handers (pianists) that means also figuring out a fingering for the hand that does not play the particular problem passage as well (while you're there, make it an even work-out:-)
Much past freshman year, I think testing of those basics is a waste of time; the student is, after all, already working on a handful of pieces for exams and usually at least a few others as well, the performance of which ought to be telling enough for any adjudicator.
The ideal is nothing but private tuition, with the student developing and being pushed by the perfect pedagogue who best knows the what and when of what is next, free from meeting some standardized level per every six months -- that died the moment there were conservatories and syllabi: in that regard, any four year program, two year program (masters level) is already a somewhat damned 'one size fits all and done within X specific period of time' kinda deal.