No, its not; and its kind of odd to say that during the era when not omly does the President fully exercise that power, they have for all practical purposes had it augmented by delegation (substantively on paper, and even more broadly in practice) of Congress’ power to declare war.
It’s true that most Presidents don’t micromanage the military, but they very much do command it, and a power generally used with some discretion and reserve is not the same as a legal fiction.
But the important thing about the President’s Commander-in-Chief role is not that it is a power (though it is), but that it is a constraint on the Congressional power to orgabize and set rules for the military.
Ultimately, military grand strategy is a domain of politics as much as it is about how to wage war. The agendas and objectives are ultimately continuations of political goals of whoever is in power. During a war, the fighting must be coordinated with diplomacy, economy/trade/manufacturing and public relations/propaganda, all of which generals tend to know little about.
And even if the President is not the one making the micro decisions, he/she definitely is responsible for making sure the war is waged in a way that is aligned with the general objectives of the administration.
This means defining objectives, access to resources as well as defining the rules of engagement. And equally importantly, listen to the military and determine when the time is right to actually provide additional resources or permissions, despite political costs.
Of course, that style is a lot harder, and thus consumes a lot more limited attention.
Instead we get military generals who act more like politicians the more senior they get (proven by study). And it seems that often politicians with little to lose and a lot to prove are often more hawkish than the military around them (Hilary Clinton, Wolfowitz, et al).
But, you know, tradeoffs…
Having served in the US Navy, this statement could not be more wrong. All command authority is delegated from the President, full stop.