Holding will never improve your odds and switching will never worsen them, it's always correct to switch whether the host opens the door randomly or not.
This actually made me think of an interesting variation that has somewhat to do with weighted ranges in poker. In said variation the host knows what is behind each door but can choose, at his discretion, how often or what % he will reveal each door. Of course, the solution is anticlimactic and it's exactly what you said. always switch.