The h-index seems like much weaker metric than PageRank. For instance, consider 10 professors you decides to game this. They will create 100 fake papers and cite each other in all. Now suddenly they would have h-index of 100!

PageRank is recursive metric in graph. In above case, if above 10 professors don't have any other links pointing to them, they don't get ranked higher. PageRank was designed to eliminate scenarios like above.

It's amusing that Google Scholar doesn't use PageRank prominently instead of these weaker metrics.