Keep them coming! This is really important. In relation to the ASIC, my friends who fly a Falcon 10 in the USA do not have ASICs – they are not required.
What about this one? In Australia a student pilot needs to get an ASIC, with all of the costs and delays involved. In the USA there is no such requirement – and remember the US is the home of September 11 – the instructor simply has to check that the pilot is an American citizen by looking at a birth certificate or passport.
Djpil, you say:
I'm not sure that "most" flying training in the USA is by independent instructors
I can assure you that the latest statistics show that over 60% of training in the USA is performed by instructors who are independent of a flying school which would hold the equivalent of an AOC in Australia. That’s a good idea too, but direct training by an instructor would have great advantages in reducing costs here in Australia – especially in our more remote country towns.
As I said, keep them coming.