You have to manually mark entities though, how is this advantageous over say indexing your data using solr or whatever, and using even the built-in clustering tools? (Carrot by default)

I didn't realize solr had clustering. One difference might be the ability to pass in scoring, include, and dynamic tagging functions at clustering time. Does carrot cluster on arbitrary document fields?

I'm not sure if Carrot does, but with Solr you have to specify which fields to cluster on then restart the instance. The clustering functionality is a contrib library I believe.