So, what was Henry the VIII's problem anyway?

I don’t know about a third of the noble houses going extinct every generation, that number seems excessively high. Sometimes a ruler died without a legitimate son, and the lands were inherited by a brother, a nephew, a cousin, so the inheritance remained within the same male kingroup. The Plantagenets bred like rabbits until the War of Roses, when they started wiping themselves out. The medieval Scots dynasty made it 252 years in the direct male line, even though for the last hundred or so they were barely limping along. The Árpád dynasty of Hungary lasted from the 10th to the 14th centuries, once again in the direct male line. And of course there’s the Capetians of France, who lasted from 987 to 1830, all male-line descendants of Hugh Capet, albeit through a couple of cadet branches.