In some ways it is, but I think calling the clade "doomed" is a bit strong.
It strikes me as a bit teleological...
By that reasoning, every large-bodied clade on earth is doomed to hit extinction soon. Would you call elephants, artiodactyls, whales, ursids, etc all doomed?
Sauropods! The literally biggest success story ever. =8-)
It is worth noting that they had a worldwide distribution, despite having low taxon diversity.