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But it's extremely little additional work, though.

The application is already able to find articles around a given address. The only thing that would be changed, is that you enter the address by hand instead of letting the browser locate you. This can be easily done in a day

Unless you’re entering your location as lat/long, it’s a lot more work.

"Extra" work? Accepting manually entered locations is utterly trivial compared to using the browser's location feature.

And it would be very easy to find out how many people start the page load, and don't complete. This will be close to the number of people who cannot or will not allow their browser to divulge that information.