1. The chairman of the Fed may not be a directly elected position but is still indirectly elected, because they are appointed by the president and must be confirmed by the senate. Saying they're not democratically elected is about as true as saying the secretary of defense is not democratically elected. Technically true, but mostly irrelevant.
2. You vastly overstate the power of the chairman of the Fed. It's not like Powell can have a bad day and decide to nuke the world. He's more powerful than most people, but society hardly depends on him.
Every time we have seen a government take control over the money printing press, it ended spectacularly bad. There is a reason why most governments have agreed that the central banks need to be as impartial and independent as possible - and countries like Turkey are proving it at the moment.
Just imagine someone like the 45th being able to order the Fed around in a way similar to Erdogan. Complete, utter horror.
2. You vastly overstate the power of the chairman of the Fed. It's not like Powell can have a bad day and decide to nuke the world. He's more powerful than most people, but society hardly depends on him.