Wouldn't it be much simpler...
to pay the licence fee out of general taxation, on the basis of the existing fee times number of households? That would eliminate all the costs associated with administering, collecting and enforcing the licence fee as well as the complications with free over-75s licences. Tax threshholds would be reduced slightly to compensate.
That would automatically cover all UK citizens watching any BBC content on any device at any time in any place. It would only leave out overseas visitors, and special arrangements could be made for large hotels e.g. through a tourist tax. Small B&Bs could be disregarded.
Of course people will cry "why should I pay the licence fee if I don't watch the BBC?". They always do. But commercial tv costs us far more than the BBC licence fee and we don't have any say. And with commercial tv we have to pay for not just the programmes (mostly trash) but also the cost of making the ads (mostly annoying trash). I can't ask Sainsbury's for a discount because I don't watch their adverts or those of any brands they sell. Ditto any other shop.
Btw there is no longer any such thing as "live tv". It's all at lease two seconds old by the time we see it - more for HD.