If you think of impact as the number of people you touch multiplied by the impact you have per person, it becomes clear that the easiest way to have more impact is to touch more people. The reason is that, no matter what you do, you can only have so much impact per person because they will be interacting with you, or your good or service, for, at best, a fraction of their day.
Touching more people, in turn, requires working with more people and delegating your work to them. And the more people you work with, the more responsibility you have towards these people. Some people are held accountable by you, and you are held accountable by others. In both cases, a responsibility develops towards these people.
Fulfilling this responsibility requires sacrificing what you might want to do at any moment with what needs to be done at that moment to benefit the organization.
So at one level, you’re sacrificing your independence for impact.
However, it was your conscious decision to pursue the route of having impact in the first place. As a result, at a higher level, you’re simply sacrificing your short term independence in order to be able to pursue your long term independence.
The corollary to this is that seeking short term independence comes at the cost of your long term independence.
In other words, no matter which independence you’re optimizing for, you need to often do things you don’t want to do.