The Government have passed the administration of the licence wholly to the BBC, which means it's totally out of any democratic control. The BBC in turn can just demand any amount they feel like, and they are doing just that. If that isn't greed I don't know what is.
No they don't, the government still sets the level of the fee:
http://www.bbc.co.uk/faqs/general/licence_fee"The Government is responsible for setting the level of the licence fee and in 2016 announced that it would rise in line with inflation for five years from 1 April 2017."
The BBC is now lumbered with paying for the over 75's licenses rather than the government. They have decided not to take on this extra bill, possibly because the politicians are still prone to claim they are responsible for what is seen as A Good Thing if they do. Those same politicians aren't quite so keen on taking any responsibility to A Bad Thing.
Local councils have suffered this for years. Government is very good at coming up with half-baked ideas that suddenly become the local authorities problem to deliver, problems that don't normally come with sufficient funding to carry them out, but by that point the politician concerned has lost interest and gone back to fiddling their expenses.