Even if I had the time to read several studies and expertise to understand them, I couldn't afford it. Out of curiosity I just went to the Journal of Nutrition (I know nothing about it, picked that journal randomly) and tried to download one random issue. It was $273. Going to multiple original sources isn't practical for most of us.
I doubt that the typical mainstream journalist writing a popular story on a scientific subject could justify this expense to her boss either.
It is very often possible for journalists to get papers for free. In many cases it's easy to email the author and they'll happily provide you with a copy within short timeframes. Some archives provide free access to journalists, e.g. the cochrane library.
I'm all for open access, because I think everyone should have the right to see publicly funded scientific research. But from my experience as a journalist who's written a number of pieces on scientific works it often isn't a big problem. I never had to pay for a journal article to do my work.
I'd hope that news outlets covering any kind of science pay for access to at least some major journals as a matter of course. The subscription prices are probably much lower per issue than the price to buy an issue individually.
Most journals also show you abstracts for free, which are overviews of what each paper says. If you find a paper that you want to read in full, email the author - most scientists are very happy to know that people are interested in their work, so they'll give out copies to anyone who asks.
This isn't to defend the paywalls - I think open access is important. But I don't think the paywalls are a valid excuse for journalists.
I think the prices for most of these journals individually is enormous - they are usually sold in bundles through individually negotiated, confidential pricing agreements that run into the hundreds of thousands of dollars. Far cheaper per journal, but probably including a bunch or journals that the institution normally wouldn't be interested in, and a ton of garbage.
Not to say that many/most papers can't be found with a little bit of effort, and I can't really imagine a situation where an establishment journalist emails authors about one of their papers and doesn't get it.
If you need regular access to the scientific literature you have or make an arrangement with an institution. You don't pay per article or issue. It is a real problem for unaffiliated or freelance folks, though.
Even as a freelance person it's not a huge problem for me. It can be annoying, but if I'm doing real work rather than just looking up one article on a whim, it's not a showstopper. Mostly I just use the local university library. Non-affiliates can't check out books, but anyone can walk in and get on the wifi. And once you're on their wifi, you get whatever database access they've negotiated for their IP range. Not every university library allows this, but quite a lot do.
Its a serious problem even in academia. I have had to email authors of papers or go begging on reddit.com/r/scholar more than once, even when I had very expensive university subscriptions available to me.
Even if I had the time to read several studies and expertise to understand them, I couldn't afford it. Out of curiosity I just went to the Journal of Nutrition (I know nothing about it, picked that journal randomly) and tried to download one random issue. It was $273. Going to multiple original sources isn't practical for most of us.
I doubt that the typical mainstream journalist writing a popular story on a scientific subject could justify this expense to her boss either.