My son is doing a Level 3 OCR Extended Diploma in Business - which is the equivalent of the BTEC, just a different award route.
It's appropriately challenging, and has to be, because he's on course to get 144 UCAS points from it, which will easily ensure he can go on to Level 4 (undergraduate degree) study at university.
The coursework element is particularly intense, and he will sit 4 exams this year in total, having done a couple last year. The course content is also fairly advanced really - economics, law, ethics, accounting, sustainability, sales, marketing... Not in huge depth, but it's not a walk in the park either.
So no, I don't think it's unreasonable for there to be a requirement to have 4 GCSEs. Your son is unfortunately in the Find Out stage of Fucking Around, and I say this with some sympathy because I have always found it baffling that we put teenagers under such tremendous pressure to set themselves up for The Whole Of The Rest Of Their Life when, developmentally, many of them are the least equipped to deal with that in terms of maturity and hormones and whatnot.
Your son sounds like a bright lad really - he will find his path.