The BBC has its flaws- definite political bias- obviously since the government currently has BBC's balls in its grip. And some shite shows like Mrs Browns Boys- the least said the better!
However, David Attenborough's documentary highlighting the problem of plastic in our oceans has arguably changed the way this country and the world produces plastic forever, and made a genuine difference. Huge companies like Starbucks and others are now using paper straws for one tiny example. This alone would be enough to justify the license fee which after all isn't a huge amount.
Also there have been some really good dramas over recent years, like Apple Tree Yard, and so on, alongside the family type entertainment.
The radio stations are all really varied and cater for all tastes, and the BBC Sounds / podcasts cater for any whim- you can literally learn about anything you choose.
I have Radio 4 on all day and value it greatly. I have to watch Channel 4 news to give myself a balance though.
I think the main problem is how the license fee is presented to us, and how it is enforced. If it was rolled into our income tax, we would be less likely to complain or even notice the outlay I suspect. The officious manner of the people who come to check is unnecessary.