Once we qualify the scope of "omnipotence", is it meaningful?

I've often heard advice not to engage in all-or-none thinking. But some words seem to exist for the sole purpose of saying, "this is about all." One such word is "omnipotence," used to speak of God being all-powerful, or able to do anything. I think most people would accept "able to do anything that isn't inherently impossible" as a reasonable understanding, rather than a backdoor or escape route.

Is it possible to give billions of people the "image of God" -- including ability to shape our own surroundings and paths -- and have God remain in control of everything? In a discussion on omnipotence, either our mastery over our environment is an illusion -- we are simply God's proxies -- or God has granted us our own domain where we are agents in some real sense.

There are many kinds of evil in this world caused by people: caused by hatred, malice, greed, lust, unfaithfulness, indifference, arrogance, and a whole series of problems that need no introduction to those who have lived enough years. If God is good and can do all things, why not prevent people from harming each other by a use of his power? Typically, Christians view this as God choosing to limit the extent of his control -- a choice that was inherent in the act of creating sentient beings -- in which he gives us an area where we are in charge, for good or ill.

But once we think of God as holding himself back, once we think of billions of agents who are not God's proxies -- is the word "omnipotent" still applicable? A crude understanding of "omnipotent" is no longer accurate; for accuracy, it has to be qualified. And if it is qualified, it is no longer simply "all". Without 'all', whatever is left may not be 'none' but it also isn't 'all'.

Theologians can discuss the intricacies of God's power and speak of the subtleties of "omnipotence". But once there are subtleties involved, is the popular meaning void?