> Given user reports and experiences of Google DNS, it seems at least its stated aim is barely satisfied in the general case: it is often slower than local ISP servers.

I don't think the claim is being made that it's better in all cases. As I understand it, Google DNS is (positioned as) a secure, ad-free resolver, and tries to be as fast as possible. In practice if there is a better resolver - say, run by your ISP - for you to use, you should use that. But often ISP resolvers fail in one dimension or another, in which case Google DNS is available as a viable alternative.

Incidentally, to your question of what data is being collected: https://developers.google.com/speed/public-dns/privacy

> Similarly, sticking a proxy between a user and their destination may add more latency than it could ever save, leading me to somewhat doubt the public reason these services exist.

Again, in the general case that might be true. I wouldn't want to use a SPDY proxy on my desktop at home, for example, as it wouldn't be able to offer me any speedup. But it's already known that similar services can provide significant benefits on mobile - look at Opera Mini. Useful feature != beneficial for everyone.