The BBC could probably shut the licence fee debate down if it was able to make part of its huge back catalogue available for free if you have a licence fee number. Albeit commercial rivals would probably scream about unfair competition etc etc.
This always gets raised. Reality is that you have to charge extra for a large chunk of the library - as almost all archive, stills, music rights, writers fees, actors agreements, music performance rights, dancers rights etc contained within a show are currently only negotiated for UK TX + 30 day streaming/download iPlayer windows (unless the show is a co-pro or acquired in advance - then the income from this offsets the additional rights costs)
These rights contracts don't allow the BBC to continue to provide the content after this period without either paying again, or paying more in the first place. It's even worse for old shows - as they often had worse, not better, rights contracts in place.
There is very little output the BBC could offer indefinitely online without it costing more money. These fees are paid when the BBC sells a show commercially to another broadcaster, or when it sells it on DVD, Blu-ray or by download.
Charlie Brooker did a good explainer here :
https://www.youtube.com/watch?v=LbrmaeiZ4RE (Ironically the YouTube copy no doubt ignores the rights implications...)