None of the Lunar satrapies are under their original ruling dynasty. The Rastar-inning have held Karasal for about 120 years, which is the longest of any of the ruling dynasties. The most recent takeover was 50 years ago, when the Yanorias-ilart took over the Doblian satrapy.
That doesn’t mean there haven’t been Dart Competitions in the Seventh Wane. Quite the contrary, if anything there have been more, and often for higher stakes. The Red Emperor himself was killed in a Dart Competition in 1607. More likely the rarity of regime changes are a result of the greater proficiency all houses have in playing Dart Competitions – which the Red Emperor says is proof that they serve their function.
Is there anything to stop Dart Competitions getting completely out of hand to the detriment of the empire? If your Dart Competition screws with your payment of taxes, out come the Tax Demons.
When these Dart Competitions get out of hand – things get bad. But there’s also a strong social and religious expectation that only the elites should even be aware of them.