They have plenty of influence for developers, which means they have influence for consumers. They have a huge say in what apps and websites get built and how because everybody has to play by their rules to get on their lucrative platform. Do you think you could launch a successful search engine today that wasn't available on iOS?
Take Safari as a case in point. Apple doesn't allow other browsers on their platform which means webdevs have been limited to the parts of the web stack that Apple supports. Which, until recently, was falling pretty far behind the state of the art.