“Lead by influence” needs to go away and the earth salted where it lands. It’s bad management practice and a recipe to manufacture burnout. It’s also what nearly every high-level IC at every company I’ve ever worked at and/or consulted for has been told. Call it what it is: responsibility without authority.
The idea that this isn’t completely insane persists because you get small companies with early employees that stick around. They accumulate social capital, backchannels, know the “real person” responsible for a thing on the far side of the company, etc and they manage to produce results where nobody else can. That’s because management/leadership has effectively failed and this person has accumulated enough systems and coping mechanisms to make up for it. Then you hire someone meant to do the same role and that person reasonably asks “What authority do I have to make sure these things happen?” -> “Well. None. You’re leading through ‘influence’.” Then very predictably they flounder for 18-24 months, ship nothing, and leave the company miserable.
I can tell you with certainty what happens when a person has the choice of doing what their manager says (The person who decides their performance and money) vs the person in their DMs asking very nicely.
It’s insidious because it effectively lets the people with the actual accountability (leadership) launder their responsibility away (executing the organization’s goals) on people who hold none of the systemic levers. If the ‘influencer’ fails, that’s an individual’s fault, not the system’s.