Getting a little outside my area of knowledge at this point, but my understanding is the main reason is that clades allow for much more granularity than the Linnean taxonomic system. Linnean classification gives a maximum of 7 ways of classifying a species, while clades are only limited by the number of scientifically sound distinctions you can make between groups of species and their ancestors/descendants.

Example: check out the wikispecies entry for mallards, which are part of 40+ clades (hit the expand link under the Taxonavigation heading)