Sorry, but clearly I couldn't disagree more, and I'm sorry to start a flame war, but you don't really have much of an argument.
It's complelty chicken and egg - your example, classic FM, has problems because the BBC plays classical music (on Radio 3, unless I'm mistaken).
I listen to plenty of commerical. In fact, with the exception of the excellent 5live (which I think should never NOT be a state owed station), I try to only listen to commerical radio - and yes, it has been dumbed down, because every time any one does anything decent, up the comes the BBC, copies it's format, throws a ton of money at it, then steals it's audience. For every BBC station (even 5live) there is a commerical alternative. The trouble is, only the BBC can afford natational licenses, so any local output (mostly London), doesn't really stand a chance.
I'll be honest though, I do only know about "indie" genre stations, and again - I'm afriad your argument is not right - XFM was producing 6music esk output, well before 6 appeared (in fact, 6 stole half it's presenters) - it was had unsigned shows (still does) and broke plenty of bands. It had to chop and change once 6 turned up, and yes it isn't as good, but the format (6music) is commerically viable. Virgin lost it's way, but since it has been bought by absolute, it's starting to change for the better, producing bespoke 80s and 90s rock/indie esk only DAB stations, along with more specialist shows starting to appear in the evenings (not as good as 6music, but you have to cater for the audience don't you). This non commerical argument is a myth, as is the origionaility of 6music's output (but as I said, 6 should survive, and the others, at the expense of radio 1 - come on, what of educate, entertain or inform does radio 1 actually manage - have you listened to Moyles!?)
Rergardless though - are you telling me that this ringfenced "educate, entertain and inform" charter would be dumbed down by playing 60seconds of ads every half hour?! The BBC floods it's radio with self promotion as it is, it really wouldn't hurt to have that in there and save some of that wasted money.
And I never said the BBC should broadcast un-popular output. Just said output that couldn't exisit in the commerical world (Most of R1 could, most of 2 could - the parts that couldn't, then fair enough, create a channel for it). Ideally, I think the BBC should quit radio as a producer/broadcaster, and live as a platform to assit other stations (including it's own current lot) - letting everyone have a fair stab a the pie.
Still, with the days on podcasts, on demand music, etc. I can't see much of the BBC lasting much longer.