No, they would rather people had a choice of more than one good smartphone to buy. If you think that the people in Google think that there's any hope of 'killing the iPhone' then you're mad. Android is an alternative and by adding competition it forces all phone makers to up their game. Google makes almost no money off Android as far as I know, but it does make money from people using web search and clicking on ads, whatever device they do it from (assuming they use Google's search engine).
If Google made money selling it's handsets, like Apple does with the iPhone, I might agree with your reasoning, but it doesn't. The two companies have two distinct revenue models and in Google's case it doesn't want or need a monopoly on the phones people use.