I wonder if this is part of the broader argument along the lines of "I don't have kids so why should I pay for schools?" Some people's view that they should only pay for exactly what they use is so entrenched that it's difficult to even have that conversation. The schools argument you can kind of see, but what about fire? Police? Street lights? Where does it end?
Over the weekend I saw a discussion about a glimpse into what a post-licence fee world would look like, in the form of adverts running during the Six Nations rugby coverage on ITV (as in, during the actual period of play). It's not hard to imagine that getting worse, without ad-free coverage from the BBC to compare against.
I do believe there should be some kind of national broadcaster in each country, but I also agree the system isn't perfect like it is.