The reason is that the tools used to compile OSM data for Garmin devices don't know how to create the address database that Garmin uses in it's own maps. There is a workaround or two:
1) Most street names are created as Points of Interest - so if you go Navigate -> Near (target city) -> Point of Interest -> Spell (enter road) you should get close
2) You can also simply go Navigate -> Near (target city) -> Browse map, and select the road target yourself.
The downside is you can't do any kind of postcode search
I've just come back from a holiday in Western Canada, and used OSM to route my way around. OSM isn't as good as maps produced specifically for a device, but for me, it's good enough, and has the bonus of being community-created
You can read more about the Garmin address problem on the "mkgmap" mailing lists, if you're interested.