How else do you expect to fill the four channels 24 hours a day without having repeats. If you look at the Freeview line-up, over a hundred channels, all full of repeats or utter garbage. Financialy it is just not possible to provide a full service 24/7. Also, where do you find the programs ?
'I have to ask what does the BBC spend the licence fee payers money on'
That is the wrong question. You should be asking what the licence fee would need to be for all output to be brand new and shown only once. I do know the answer except that it is much higher than people would be willing to pay.
But, I'm with spider9. I find repeats helpful and the fact that content may be available on iPlayer doesn't mean you don't need repeats. It just adds to choice.
Of course, I wish they wouldn't repeat 'The Voice' but that's because I wish they didn't show it the first time.
In other words, I don't think anyone has an objective view about repeats. The BBC can repeat things I like to watch as many times as it wants.