For those times it doesn't work, I check if it's on Archive.today[0]
They opensourced (some) of the logic used for how it works
If anyone has any contact with the NYTimes ops' team perhaps this issue could be raised with them.
I never hit a "paywall" when reading NYT via the commandline.
"I've noticed sometimes if you hit the paywall and then try a different browser the paywall is still there."
If stop using a popular "browser", then it is gone.
A couple of easy ways to get NYT article URLs
1. Sitemaps, e.g.,
https://www.nytimes.com/sitemaps/new/sitemap-2022-01.xml.gz
https://www.nytimes.com/sitemaps/new/sitemap-2022-02.xml.gz
https://www.nytimes.com/sitemaps/new/sitemap-2022-03.xml.gz
https://www.nytimes.com/sitemaps/new/sitemap-2022-04.xml.gz
https://www.nytimes.com/sitemaps/new/sitemap-2022-05.xml.gz
https://www.nytimes.com/sitemaps/new/sitemap-2022-06.xml.gz
https://www.nytimes.com/sitemaps/new/sitemap-2022-07.xml.gz
https://www.nytimes.com/sitemaps/new/sitemap-2022-08.xml.gz
https://www.nytimes.com/sitemaps/new/sitemap-2022-09.xml.gz
https://www.nytimes.com/sitemaps/new/sitemap-1975-01.xml.gz
https://www.nytimes.com/sitemaps/new/sitemap-1975-02.xml.gz
https://www.nytimes.com/sitemaps/new/sitemap-1975-03.xml.gz
https://www.nytimes.com/sitemaps/new/sitemap-1975-04.xml.gz
https://www.nytimes.com/sitemaps/new/sitemap-1975-05.xml.gz
https://www.nytimes.com/sitemaps/new/sitemap-1975-06.xml.gz
https://www.nytimes.com/sitemaps/new/sitemap-1975-07.xml.gz
https://www.nytimes.com/sitemaps/new/sitemap-1975-08.xml.gz
https://www.nytimes.com/sitemaps/new/sitemap-1975-09.xml.gz
https://www.nytimes.com/sitemaps/new/sitemap-1975-10.xml.gz
https://www.nytimes.com/sitemaps/new/sitemap-1975-11.xml.gz
https://www.nytimes.com/sitemaps/new/sitemap-1975-12.xml.gz
2. JSONP https://static01.nyt.com/services/json/sectionfronts/$1/index.jsonp
where $1 is one of the following fashion
crosswords
us
briefing
sports
opinion
magazine
theater
style
business
technology
realestate
t-magazine
climate
nyregion
arts
obituaries
dining
health
briefing
well
learning
science
It is possible that this question is being asked because the submitter wants to try to annoy www users with a "paywall" like the one used by the NYT. Let's hope not.