Is the threat of a coup the fundamental weakness in all military systems?

In order to have a good military, the chain of command must be without a kink in the chain. Everyone has to follow orders, otherwise there is confusion and chaos.





In a coup, the enemy takes over the head of the military and becomes the official leader of the military. The soldiers must now follow their enemies, otherwise they will be accused of mutiny and treason. So long as it is a successful coup, and the leader is given full credit and authority by the higher ups, the military is now under his command whether he was the enemy or not. Is this the fundamental flaw of all military systems?|||Kind of a fundamental weakness in any institution run by people.