Well, there’s Safari but that’s for apple only, and technically they don’t really control chromium-based browsers - they’d have to do yet another cycle of EEE to actually kill of competition. And firefox can survive without google for a while by downsizing massively and focusing on chinese market as they still have that baidu deal AFAIK.
But overall, yes, Google has in fact cemented themselves as the middlemen for all things internet, on both mobile and desktop.