It's already happened. More and more news sites are behind paywalls. A lot of the articles posted on HN are behind paywalls, and half the time I'm too lazy to try archive.is or one of the other paywall workarounds, so I end up doing without.
On the other hand, if I'm reading an aggregator like Google News, the interesting thing is that the top article for a particular sub-topic might be from the NYT or another site with a paywall, but if you look down the list you can get a similar article from a non-paywalled site. The cool thing about this is I get exposed to a bunch of random sources, and often they are local news sites.
I've looked into subscribing to some sites, but most want north of $10 per month, some in the $20-$30 per month range, and I just don't get that much value out of them to justify paying, especially when I'd end up having to pay for several of them, which would add up to several hundred dollars a month. It's still a real shame that micropayments isn't a thing; I wouldn't have an issue reading the first paragraph or two of an article, and then having to spend something like 5c to 25c to read more. I fully understand why micropayments haven't taken off, but it's a shame nonetheless.