Why was Stoicism so attractive to wealthy and powerful Romans?

The most fascinating figure, to me, in Tacitus' Annales was Seneca. This is a legit well known famous philosopher (as in, famous for his philosophical teachings) who ruled the Empire for a solid five years by guiding the thinking of Nero. That's a very strange combination. This is one of the Empire's more bloodthirsty and insane rulers, who, for five ye…