I wonder what Google's getting at here?
This tool is just an extension of how Google Analytics fits into their strategy: by making website owners smarter, they will be more willing to build better websites and spend ad dollars driving traffic. If you have no idea what your website is doing, you have no incentive to acquire traffic. Make a better website, grow your visits? Google still profits. This explains why GA is free -- you can better measure the ROI of your ad spend and will likely spend even more.
Nope, it is to make sure the user still needs to search for web sites.
> Almost every Google product and service has been around encouraging consumer use of the web, or fostering growth of web businesses.
Are you kidding? How do scary display ads (matching the user's recent e-mails) encourage consumer use of the web? How does going into many established business areas (product search, classifieds, insurance price comparisons, social networks ...) foster growth of web businesses?
> Make a better website, grow your visits? Google still profits.
Unless that website competes with Google ... Does Google profit from Facebook's growth? Nope, so they tried very hard to force G+ down everyone's throat.
As for why GA is still free - you must be working at Google, otherwise I can't explain your bias. GA is free because it gives Google important information, for example which websites are most popular (good for providing helpful search results).