They don't care, what they're absolutely terrified is another Arab Spring happening at home.
The bet is that no matter who is in power, the ruling classes won't find themselves under the boot, which is a pretty good bet to make. Beats a revolution, in their eyes.
A person doesn't need to be elite to be terrified that something like Arab Spring will happen in their own country: the Arab Spring was really terrible for ordinary people: millions violently killed, millions of refugees, over ten million made homeless. In Syria, the mass killing is still going on.
(I'm surprised anyone still calls it the Arab Spring now that we know how disastrously it turned out.)
The bet is that no matter who is in power, the ruling classes won't find themselves under the boot, which is a pretty good bet to make. Beats a revolution, in their eyes.