We also lose a useful term if we define it that broadly, though. It's not only an economic system, but a complete political/economic system that comes with a set of aesthetics and a particular focus on nationalism, a strong state, and a strong leader.

Just government control of nominally private enterprises is much more common than fascist regimes; it'd also include the UK in the heydey of the East India Company, modern-day China, and even to some extent modern-day France.

The problem with that definition is that it also defines rather well most available instances of Communist states. So are you saying Fascism=Communism? Or that those states are not exemplars of "real" Communism but are in fact exemplars of Fascism?

Berlusconi's Italy might also qualify.

You yourself demonstrate nicely that to many, the term is "useful" only as partisan political ammunition, for your "definition" excludes so many of the defining features of fascism (nationalism, authoritarianism, militarism) that it is completely meaningless.