They realize that if the whole house of cards collapses they're loosing the most. If the house of cards (the system) is stable they're better off as well.
Are you sure about that? Well... for Dalio, he's an investor that is always looking both forward and backwards. He's looking backwards to see what's happend in the past and how economy/society has reacted. He's looking in the future to see how he could best take advantage of signals he sees.
This seems to be the deeper reason why many wealthy people begin leaning left publicly after amassing their fortune. The very same people can often be seen years earlier making statements that could come out of an Ayn Rand book, but when they’ve beaten the game, the risk-mitigating option is to become “the people’s billionaire.” Im afraid it’s not a change of heart, it’s simply the most logical decision for someone whose wealth is locked up in institutions governed by a democracy.