I wonder if we disagree. You aver that "You can't influence people if they don't trust you." If you really mean what you say, then we must disagree. Of course we can be influenced by people who don't trust you. It happens every day.

They influence with guns. Not only directly but also with the mere threat. (If there were no threats, would we build defenses, avoid dangerous places, or arm ourselves - all indices of reactions to influence).

They influence us with force of law (in essence, with the guns wielded by our own government).

They influence us with paychecks. I may not trust you and firmly believe that you are leading us to perdition, but I'll follow until the paychecks stop coming (especially in these days when paychecks are very tenuous things). Sadly, I have watched the employees of many corporations march in lockstep behind leaders who led them into the abyss of financial ruin despite warnings born of their own good common sense.

Now, if you care to distinguish between good and bad influences, good and bad management, good and bad leadership, I'll be happy to concur. Until then, I'll take my own path...