Yes, I think promoting people who DO NOT complain is problematic.
There is no right way to deal with this other than to listen to complains and figure out what it is.
One way of thinking about complaining is that it is a form of feedback. As a manager, you don't want to silence people giving you feedback, frankly, this is about as stupid thing as you can do.
Better way to deal with complaints is to educate on what kind of complaints are productive and what kinds are destructive.
For example, I try (not always succeed) to restrict to myself to only complain about things that I am ready to solve if somebody tells me "go ahead, fix it".
There is no right way to deal with this other than to listen to complains and figure out what it is.
One way of thinking about complaining is that it is a form of feedback. As a manager, you don't want to silence people giving you feedback, frankly, this is about as stupid thing as you can do.
Better way to deal with complaints is to educate on what kind of complaints are productive and what kinds are destructive.
For example, I try (not always succeed) to restrict to myself to only complain about things that I am ready to solve if somebody tells me "go ahead, fix it".