There are a lot of reasons Google provides this data for free, but mostly it comes down to these two:
First, they use the data too. The more sites they put their Analytics code on, the more data they have about how people tend to use the web, and the better they can make their services. They even can try to pair people's search behavior with their on-site behavior to see how different test algorithms might be affecting the usefulness of their search.
Second, it helps us all make the web a better place to find data, which in turn helps Google. It's hard to deny that Google is the door into the web for almost every American, which means every way they can improve the web experience is beneficial for them.
It's also worth noting that while Google is giving us a lot of their data processing power, there is an upper limit. When you hit that, you need to switch to Analytics Premium, which gives you high priority processing and an unlimited number of "sends" to the Google Analytics servers.