Just a nit - calling the NYT a "regional publication" is like calling Google a "california search engine." It's one of the largest global news organizations in the world with active newsrooms in NYC, London, Hong Kong and Paris. It has 6 news bureaus in the NY area, 14 news bureaus in the US outside of the NY area and 23 international news bureaus employing over 1300 news staff. (For reference the BBC has 50, CNN has 32 and the Times' has 46). Its California coverage is as robust as the LATimes and more robust than the SF Chronicle.
Of course, when you have multiple full newsrooms, you care about location capabilities. I get a customized California feed (California Today) when I go to it.
Again, this doesn't really compare to Google - if somebody started up a business within Google and only had about New York Times level of success, it may very well be in danger of being shut down. New York Times has about 3 million subscribers. Youtube Premium had 1.5M about a year after launch and it's on life support. Youtube Music has 16 million subscribers a year after launch and it's barely successful enough not to be cut. These are ancillary services run by small teams. Google has Android, Chrome, Search, GMail, Maps, Photos, Calendar, etc, etc, many of them actually manage lots of your data on your behalf and/or require real-time location capabilities. Of course providing these services requires a long privacy policy if they want to honestly cover what they do with user data.
"California Today" needing a location capability - I'm not sure if you're entirely serious. Why would it need to access your current location - people read local news for where they live, not where they happen to be. And whether you're in California or not is not something that changes frequently. Nor is California Today a travel guide - it has no relevance for people who happen to be in California. Do you actually know if it's based on your real time location? I doubt it. And even if it was, it doesn't have to be.
Also looking at this - https://www.nytimes.com/column/california-today - it consists of an article every other day or so? This is why they need the location data? And it doesn't look like it's a customized feed at all - seems like everyone gets the exact same feed. What data do they need to put this together? And it looks like they have a signup sheet - https://www.nytimes.com/newsletters/signup/CA - are you sure they don't automatically sign you up based on your permanent address? I mean, consider the level of location access (frequency and granularity) needed to show New York news vs California news and compare that against, say, turn-by-turn navigation.
Also I just downloaded the app and it has "Australia" as a top-level section by default (I'm in the US). Are you sure user location is used meaningfully for anything in the app?
Of course, when you have multiple full newsrooms, you care about location capabilities. I get a customized California feed (California Today) when I go to it.