"The Peter principle is a concept in management developed by Laurence J. Peter, which observes that people in a hierarchy tend to rise to their "level of incompetence".
As a politician he was a great bodybuilder. He was eventually promoted to his level of incompetence.
Arnold's jobs were pretty easy, all things considered: Lifting weights, having someone ghostwrite his book while he dictated it out loud, playing tough-guy roles with minimal emotional depth or memorization, and co-owning a gimmick restaurant (Planet Hollywood) that went belly-up.
Governing a state is a tough job. He proved he wasn't equal to it on the basis of his management alone, to say nothing of his non-existent credentials outside Hollywood and Gold's gym. The same could be said of George W. Bush or Donald Trump for the Presidency; the difference is Trump is a born salesman who gets restless and bored counting his money or hitting golf balls at his various resorts, and felt no one on the Republican side truly captured the grievances, complaints, and hopes of the people who ultimately chose him over other established figures like Ted Cruz and Chris Christie, who had real political and campaign experience. He also held his own in tough debates with better-educated and faster-thinking people in his party, and later with one of the most formidable political figures the left had available at the time, not to mention her nearly-universal support from women and minorities, which he doesn't have. For being nearly 2 years in office, he's held his own very well against a globally hostile media and half the country praying for his downfall, a federal government with hunt, a corrupt former FBI director and middle-management agents who got caught red-handed plotting against him in text messages, and junk lawsuits by disgruntled, lying women who are trying to capitalize on his fame and power by hiring slip-and-fall lawyers that prostitute themselves out for 5 minute interviews on every liberal outlet. This guy's got the weight of the world on his shoulders with Iran and North Korea threatening us while the Canadians, Europeans, and Chinese do nothing but obstruct or cry about unfair tariffs while imposing some of the harshest ones of their own against the U.S.