The influence of Chrome and Android on web development are very probably part of what Google is aiming for. It's the anti-Facebook/Apple, in a way, which should help Google Search keep earning enough money to support all the other peripheral projects.
I read recently that 90% of HTTPS traffic for Google properties <> Chrome is handled using SPDY. Interesting also that Google continues to put more and more of their properties on HTTPS.
I think Chrome is useful for them for just this reason, rather than solely trying to cajole others, they can just do things. I imagine this will continue to accrue benefits to them for quite some time.