I think the BBC is absolutely comparable to education and healthcare - , but if you like, how about municipal services? Who needs swimming pools or libraries?
The BBC is an entertainment broadcaster - it's not remotely comparable to public facilities like pools and libraries!
Besides, people pay to get into swimming pools and leisure centres. You wouldn't be happy if you had to, say, pay for your neighbours gym membership or their DC's swimming lessons, would you? Libraries are funded by their local councils/taxes and often run activities like toddler classes or have cafes to help with the costs. They also charge for printing/photocopying.
You wouldn't pay my SKY subscription so why should I pay for you to access the BBC?