Google got big when being a dot-com URL meant something and the primary way the average person accessed the Internet was through a desktop PC. Neither of those things is true anymore.
I don't think people associate search with an app. Search is something built in to the operating system or browser (a distinction which is disappearing too).
People use apps more than they use a browser. It's not a big deal to reform search to be an app, it will be natural. People listen to podcasts without knowing anything about mp3 files or file systems, they edit and upload their photos without knowing about jpegs, etc.
