For this discussion, let's make a distinction between "independently wealthy" and "financially independent". Per my thinking, the former describes people who possess more wealth than they can spend, while the latter is a more readily attainable state. If we can agree that "financially independent" describes people who have sufficient resources to meet their needs, then this type of independence becomes a goal we can plan for.
Ultimately, in the pursuit of financial independence, the goal is to have enough money set aside and working hard for you 24 / 7 that the produce of those savings is sufficient to cover your core budget.
So while we all take the July 4 holiday as a time to appreciate our great country and all that it represents, on July 5 maybe take a moment to consider whether financial independence is a goal worth pursuing.