If, in my Peak State theory, the chief puppetmaster in a Deep State is more likely to be the public top guy (or, in case of term limits, the obvious de facto top guy, like Putin in Russia) than anybody else, how can we account for assassinations? For example, Pakistani president General Zia-al-Haq's airplane fell out of the sky in 1988 in a highly suspicious manner.

Well, assassinations of the top guy show that it is important enough to be the top guy that other guys will risk their lives to kill the top guy.