Agreed, I don't mind the license fee because the few programmes that I do watch are ad free, sponsor free and in my opinion high quality. I'm happy to part with my money for MOTD, Top Gear, the Attenborough wildlife programmes, BBC News, the extensive BBC website, iPlayer, Panorama, some International football, new Family Guy, new American Dad etc. Banner and ad blockers are becoming more popular on the internet; the user's experience without the crap is better.
If funded by adverts there's nothing to suggest the programmes you've said you watch wouldn't be made anyway, it's drama that would probably take the biggest hit.
My biggest gripe with BBC isn't the license fee (which I think should be incorporated into taxes that everyone pays, such as VAT). It's the amount of cross platform BBC advertising, it seems to be increasing as well as the number of repeats on the same day - especially on radio!
Having a separate license fee with staff having to chase up non-payment, processing of that license etc all adds cost. Surely it'd be far more efficient to take it from an existing tax which is then raised slightly to compensate. I've suggested VAT but I'm sure there's several others which everyone pays and can't be avoided.