"In the olden days", people who couldn't afford orchestral instruments made music on whatever they had to hand - paper and comb, washboard, spoons, or if they could afford an instrument, something like a harmonica. Although even poor families often had a piano, and all the family would share in the singing, for which you didn't need music, it was songs that everybody just knew.
But I think you're talking about a music education, lucky, aren't you, which I agree is to a large extent beyond the means of many families. Even with singing, where you don't have to buy an instrument, you still need lessons and repertoire books to be "musically educated", even if you don't go in for exams, festivals and the like. Somebody on a low income who wants to learn an instrument other than singing would find it even more difficult, if not impossible. Particularly if lessons are invoiced a term in advance, even half-a-term, that's a lot of money upfront for people on a low income.
There must be many children who given the opportunity could become skilled musicians, but who don't have the opportunity because they are in low-income families. Music is just one of life's opportunities which those children are denied. I remember going to a very impoverished town for the first time - the traditional industry had died out and there was high unemployment and a general sense of hopelessness and decay. I remember thinking that the children of those families didn't stand much chance of getting out of it

The notion that they could afford to take up a musical education is not realistic.
Sorry, I digress. As far as exams are concerned, I imagine the AB set the rate as low as they can in order to attract as many people to do them as possible, within the constraints of all the overheads they have to meet.