This premise fails right at the start. Why would "they" lose their power when people know about aliens? All the reasons why the current batch of political leaders are in power remain valid if aliens exist, whether they're democratically elected or authoritarian despots.
Expand upon your thoughts to comment in good faith :) This isn't reddit
Why do you attribute either opaque or transparent behavior/comms on UFOs from the power structure, if there is nothing to be gained either way by said power structure?
IF there is any discourse to be had on UFOs, power structures hiding things etc. it would be on the topic of US DoD obfuscating Next generations Weapons testing for sake of operational security. This has been a formal USAF departments initiative since the 80s, and it's very transparent initiative.
