I expect it could be made to work, but I have no doubt people would complain about it. And the license fee is not a pure private contract - there is government involvement (hence all the political arguing about whether the BBC should be allowed to increase the fee or get rid of the exemption for senior citizens). So if there's a big change that lots of people complain about then it might be blocked for political reasons even if it actually makes sense over all.
I remember paying 300 quid for a VCR and giving them a fake name and address before leaving with my JVC under my arm.
https://www.tvlicensing.co.uk/check-if-you-need-one/business...
(If you bought more than one new TV per year, your TV license account would be in perpetual credit. I don't see that as a problem.)