No... they really don't. They make a lot of money off search traffic and the app store. Android licensing amounts to approximately $0.75 per handset. That's not even a rounding error on their balance sheet, and SURELY not something to "intentionally break android" over. Broken android is a great way to drive people to other platforms. There's nothing to be gained for them in that.
more to the point, why do you think they released the Pixel line-up? They got sick of vendors screwing up Android by skinning every premium handset on the market (and skins are the primary source of broken garbage). And in that endeavor they've been wildly successful. The pixel is by far the best android handset I've ever owned. You pay for it, but it's worth it if you like android.