OSM doesn't have a cleaned up dataset of Points of Interest.
Yes and no. OSM is a database and has lots of Points of Interest, e.g. here's a Starbucks in London ( http://www.openstreetmap.org/api/0.6/node/488443269 ), so it's trivial for someone making a map app to make a database of PoIs that an application can look up.
You can easily do geocoding with the OSM data. Nominatim is ready to deploy software that will let you do both normal and reverse geocoding. It is what openstreetmap.org uses for its search box.
And nominatim is open source ( https://github.com/twain47/Nominatim ), so if there's some silly embarassing thing that it gets wrong (like the address of your headquarters), then you can fix it yourself.
True OSM doesn't have that, but there are some public domain datasets available for that, e.g. SRTM.
OSM doesn't do geocoding.
True. OSM is just a database, you'd have to make your own "address ↔ position" algorithm. Which is sorta hard.
OSM doesn't do routing.
OSM is just the database. You can (and people have) make a routing engine on top of that (e.g. http://map.project-osrm.org/ http://maps.cloudmade.com/ ). You can do very specific types of routing (e.g. I figured out how to cross Dublin without passing a pub http://www.kindle-maps.com/blog/how-to-walk-across-dublin-wi... ).
OSM doesn't do 3D.
True.
OSM doesn't have a cleaned up dataset of Points of Interest.
Yes and no. OSM is a database and has lots of Points of Interest, e.g. here's a Starbucks in London ( http://www.openstreetmap.org/api/0.6/node/488443269 ), so it's trivial for someone making a map app to make a database of PoIs that an application can look up.