You're right. There is (are?) an open source web interface to OSM. Technically, someone could host that themselves, and the app is just the web browser.

The real reason that it's not common is because there's no demand; or, at least, not enough for anyone to take the effort to package it up in an easy-to-deploy, well documented release. And demand is low because having offline, local tiles is almost always preferrable to nav or maps that require relatively heavy, constant internet access.