It's not like a manager sits down and thinks "I think being untrustworthy is going to give good results. If that doesn't work, I'll try my other idea: honesty."
Trust, or lack thereof, is formed from actions purely made for other reasons. It's a consequence, rather than a cause of action. Though some managers will sometimes act to not erode trust, but this may be at the expense of something else.
I think it's very easy to sit in a position, without feeling their set of pressures, which will be different from your own, and judge a manager for how they are acting. Without seeing the factors, it may seem like the behaviour is self-destructive.
Nobody is saying it's a good idea to have a lack of trust. But sometimes employees are very confused about what the role of their manager is. Sometimes employees will think "a manager will have my back", when instead they should recognise that a manager should provide an appropriate level of support.
For every bad behaviour you can think of, there can be an explainable reason for it, beyond a manager just deciding to be untrustworthy. I'm not saying these a good reasons, just they are reasons beyond some sort of machiavellian aim to be untrustworthy.
A few examples:
A lack of regular communication
They believe it's an appropriate level of communication already. Or they would rather not bother employees with what they view is useless detail.
Lying to employees
Sometimes bad, or even good news, can harm the team. Maybe some members of the team lack the maturity to handle the truth.
Erratic promotion procedures
The manager may not be the cause. There can be budgetary reasons, HR driven reasons, law reasons, why there may be some chaos when it comes to promotions. I also have to say that sometimes people believe they have a right to a promotion, when this is not often the case.
Favoritism to employees
They are human. They will have employees that they favourite, either for personal or professional reasons. Maybe "Bob" gets all the nasty work cause he is good with dealing with it.
Giving employees minimal support to improve or develop
There may be no budget for it, or they may be too busy.
Ignoring direct reports
Some direct reports are probably better left ignored.