The thing is Yamaha, cost is a real issue and it is why music is now such an elitist subject. If your child is good at say maths, they can go right through school and to a great uni with only the 'normal' costs to parents. If music is your child's passion and they are great at it, unless you live in one of very few areas where music is heavily subsidised, parents have to pay thousands of pounds for instruments, lessons and associated costs.
I have 3 children, 2 already taking music lessons and one starting next week. The first two have already been classed as exceptionally gifted musically and from being a nice, fun thing to do, their music has suddenly become much more serious in terms of expense. We are really struggling to afford it all, and I know families who couldn't afford even one lot of music lessons (£120 a term). This just shouldn't be the case, and it is sad that there is no consistent policy - I know LEAs that really subsidise music, while even in the next town to me the secondary school pays for instrument/voice tuition for anyone taking the GCSE music course, whereas our school doesn't.
Music shouldn't be elitist, it should be for everyone, whether that's on a fun, basic level or more advanced. But the only way to do that is to make it affordable. That in turn probably means things like shared lessons and so on. But what's actually so wrong with that, if it starts the child off on their musical journey and gives them a passion for music, or even just a liking for music! All the peripatetic teachers I know are actually well qualified and very professional. I accept there are bad ones, but I bet your life there are bad private teachers too. My son has moved onto secondary school and has a new music teacher, one who has a great reputation locally and in the wider region, and he has great respect for the peri who taught him at primary school.
Certainly one of the peris I know reckons that some of the interviews/auditions for peri jobs can be amongst the toughest for any job in music. Not only does she have to prove her practical abilities with the whole of the woodwind family, but the audition panel also watches her give sample lessons to small groups of pupils of all sorts of ability. So no resting on your laurels as a well-qualified or 'professional' musician, you really have to prove you can do the job!