> stations in remote places all over the country

s/country/world/

There are many large projects to collect this information ranging from extremely specialized satellites to networks of ocean buoys. It turns out that weather is a global phenomenon and warming seas on the other side of the planet affect wherever you are.

You're not wrong, but I would like to point out that there is also the Civilian Weather Observer Program (CWOP) that is fed by a lot of private weather stations (the kind you can buy at Walmart of Amazon and put at your house). I believe the data is aggregated and averaged to account for variations in installation deficiencies, and used to inform/enhance the government maintained data feeds.

We have good weather data because of satellites, and there are plenty of private weather sats.

The classical US ground station network is actually run by volunteers and has been seriously degrading in quality over time. Its data was identified as corrupted and useless for climatology decades ago, which is what led to the US CRN being built. Other countries however did not do an equivalent, and their networks are still very low quality. Most of the UK's network, for example, is considered unusable for climate monitoring under WMO standards (but they are still used regardless!).