OSM has a lot more data inside than the website shows - in dense shopping areas you can't zoom in far enough to see all the POIs, much less business names.
I've read before that using cached previews was done to stay accessible to less-powerful mobile devices, which would have smaller CPUs that would be taxed by rendering the native vector data. I view it as a branding disadvantage that OSM appears, from desktops, to have less info than alternatives. But that's a battle that's been had many times before, one might as well argue over paper vs plastic.