Yes, I see people define fascism similarly to that, frequently, and I don’t find it a useful definition at all, since that strikes me as pretty much the typical form of the state, following the bourgeois revolutions of the 18th through the 20th centuries. I’m not sure how you can look at the history of the US – the use of slavery, enabled by the state and by paramilitary slave patrols, in commercial agriculture in the 19th century; or the use of mixed forces of government troops, mercenaries, and vigilantes to suppress labor movements in the late 19th and early 20th century – and conclude that the convergence of private and state power is a recent development.
My definition of fascism focuses on paramilitary groups which use intimidation and physical violence against popular left organizations and against oppressed groups, which are mobilized by far-right ideology, especially nationalism. Fascist groups were organized deliberately as counters to communist, socialist, and labor organizations, and in some respects were a distorted reflection of the groups they were attacking.
Which, by the way, reminds me of one of the things that’s irritating about the insistence that the Nazis were socialist: by and large, the socialist movement was emphatically internationalist, often making efforts to encourage solidarity across national borders, and to oppose imperial wars, and you can often see “international socialism” used as almost a set phrase and appearing as the name of various journals and so forth; the “National Socialists” were, deliberately, negating what was generally understood as one of the fundamental characteristics of the socialist movement. It’s as if you had a group of people who went around poisoning and stabbing the sick and injured in their beds, who were known as “evil nurses”, and years later, people would insist that murder was an intrinsic part of nursing, because the “evil nurses” had “nurse” right in the name.
