Apple is the most profitable company in the world and consistently takes almost all of the profit in the smartphone industry. They also make a large portion of the profits in the PC world despite their relatively meager market share. Does Apple really want to expand into the sub $200, or even $100, smartphone market? Unless they do, I don't even really see Google/Android as their competitor.
I know it can be short sighted to base things on personal anecdotes, but while I don't use an iPhone myself, almost all of my friends do and they extensively use Google products ranging from Gmail, Maps, Photos and search.
Apple seems to have the best of both worlds in the current situation. They dominate the high end profitable hardware market and their users still get to benefit from Google products if they so choose. I'm not convinced that Apple would be better off if Google disappeared. Replicating all those services will be expensive.