An example of a use-case that cryptocurrencies could actually solve (anonymous micro-payments) yet none do.

I am not a cryptocurrency expert by any means. I’m barely literate in fact. Please entertain my uninformed question.

It is my understanding (misconception?) that cryptocurrencies don’t scale well. How would a cryptocurrency handle billions of micro transactions? How would such a system scale to the amount of content consumed?

Would there be many individual coins that are exchanged for a common one(s)? NYTCoin for BTC? Is there some method for handling transactions without the overhead?

It's a good question. On-chain transactions don't scale well but there are many solutions which only require on-chain transactions to fund some initial channels and then subsequently if a participant misbehaves. One additional benefit is the micro-transactions are not stored on the main blockchain, further improving privacy.

Bitcoin's lightning network is an example of this, and is currently up and running. Fees are incredibly low, currently averaging .0098 cents: https://1ml.com/statistics

I know! I'd love this system so much, but because of all the players involved, I think it'd be nearly impossible unless it were orchestrated by the government by creating a mandatory pay-to-play, ad-free, tracking-free, web option at the protocol level. ...which they'll never do.

The problem is that even after being paid, the content producers and distributors have an incentive to "double dip" by adding tracking, inline/embedded ads, sponsored content placement, etc.