It's so strange that in most countries, you never see someone sitting on two chairs.

The board is there to keep the company management in check. But in the US, this seems like the norm. Does it not worry the stockholders?

In the US I frequently see this:

Guy hired as CEO

Guy gets such absurd compensation he becomes a near billionaire and major stockholder after ~5 years.

Guy is elected to the board for his amazing credentials (billionaire major stockholder)

Retires at 40 to being a "full time" board member, and chills around company the rest of his life swimming in money and free shit

Pay each player $50