The clever part from Google's perspective is that you have to trade one of these things to Google in order to get access to sites that do not belong to Google at all. Google convinced site owners to have their users pay a tax to Google.
When someone uses a recaptcha, they should think about why they are doing so. It's one thing to use it to save a business model, but it's another to use it to protect information that should be free anyway. The elephant in the room is government data. Many government agencies think that selling their data can be a nice source of side revenue, and a recaptcha is a good way of enforcing it. In reality, they just increase the costs for everyone, and those with means can obtain the information while those without means cannot.
Governments need to release their data, freely, without captchas or fees for single users and bulk users, no exceptions.
The counter argument is that they do a great job with trivial stuff like registered dog's names, and less well with sensitive/important issues like policing.
What's the right way to leverage the platform developed for the first into the second?
Totally agree. Fortunately the Dutch government is trying to make as much data open as they reasonably can, and regularly organise events to encourage developers to use their open APIs.