"My door is always open" is just a way of making others responsible for noticing and reporting problems you should be on top of. It absolves you of paying attention, of taking the time to ask and listen. It's pretending to be accessible.
Don't be surprised when few people come through your open door : no one likes to be forced to complain.
Doors work both ways: if you have an open door policy, walk out and talk to your team. Actively seek them out, get to know the group to get a baseline to compare to when things go wrong, understand their dynamics, find out what matters.
And when they see you use the open door, they will be more likely to use it themselves.