The effort of the American Right to coopt libertarian identity (one of a series of such attempts that arose in an effort to regain electoral ground in the realignment after the rise of the New Deal Coalition -- including the effort to coopt white racial identity in the Southern Strategy, and the effort to coopt Christian religious identity thereafter) clearly has met with some success.
In the real world, however, right authoritarianism and left libertarianism are real things.
> Fascism, communism, nazism, socialism, etc, are subsets of leftism/statism.
They are generally subsets of statism (presuming by "communism" you mean Leninism and its descendants; with Marxism-qua-Marxism the issue is less clear, and "communism" is even more general and includes some things which are probably more accurately seen as left-libertarian), but only some subsets of that list have any real relationship to the left.
Fascism and Nazism are probably best seen as pure authoritarian; each borrows rhetorical approaches from both the Left and the Right to support authoritarianism, but neither really orients toward the Right or Left in anyway that is distinguishable from its orientation toward authoritarianism, except perhaps to the extent that one sees nationalism vs. internationalism as tied to the right/left divide (there's some traditional association of nationalism with the Right and internationalism with the Left), as both Nazism and Fascism are strongly nationalist.
> There's also the growth of institutional power that characterizes much of Fascism; that's usually associated with the Left
No, growth in institutional power is not "usually associated with the Left". Left and Right differ on who holds power and how it is used, authoritarian vs. libertarian split on the degree of institutional power.
In a sense, libertarian and left are both different generalizations of classical liberalism to a new environment -- in the environment in which classical liberalism arose, political and economic power were conjoined and distributing political power was equivalent to distributing economic power. Libertarianism (in ideal -- practical effects may differ) focusses on continuing distribution of formal political power by limiting the power of central political institutions even as economic power has become increasingly divorced from the central institutions, Leftism (again, in ideal) focusses on continuing distribution of economic power among individuals irrespective of whether its present locus in central political institutions or not.
Leftists will generally argue that distributing economic power is the best way of distributing political power, while Libertarians will argue the reverse.
That's true, but you didn't mention that prior to distributing economic power equally, leftists must first centralize it. Further, as a means of administrating the continued equitable distribution of monies, political power is gathered in institutions.
That's not the only reason, though; many leftists do not actually believe in distributing political power at all. The position that the state has a complete monopoly on the use of force is an example of this.
> That's true, but you didn't mention that prior to distributing economic power equally, leftists must first centralize it.
I didn't mention lots of practical issues that might occur in implementing left or libertarian views. But that certainly isn't a requirement of left ideology in general, though there are specific left viewpoints that favor some form of consolidation as a means to distribution (left libertarians, which are an important and growing group, clearly do not generally favor consolidation even as an instrumental means to distribution.)
> That's not the only reason, though; many leftists do not actually believe in distributing political power at all.
There's certainly leftists who believe that liberalism through the establishment of democratic accountability of the State to the citizenry has already, in many cases, acheived the desirable distribution of formal political power so that the focus should not longer be on that, such that further distribution of such power is no longer desirable and may be counterproductive, sure. There are also leftists who don't believe that.
(The same is true, mutatis mutandis, with libertarians vis-a-vis economic power by way of its divorce from control by formal political power in many modern states.)
> The position that the state has a complete monopoly on the use of force is an example of this.
The position that the State is defined as an entity that has a monopoly on the legitimate use of force is a concept which predates the existence of leftism as a distinct offshoot of classical liberalism (and probably predates classical liberalism as well.) This definition of what the State is is not an example of anything in any ideology, since its not a value statement.
Insofar as some leftists (though neither hardcore left libertarians nor communists in the vein of Marx and Engels, both of whom believe in the ultimate abolition of the State) hold that the existence of a State as so defined is desirable, this indicates that there are limits to how much those leftists believe that centralized political power should be limited by reducing the power of institutions instead of distributing control over institutions, but even that is different from demonstrating an absence of a belief in "distributing political power at all".
> Same question, how could a stateless communism possibly work?
In even Marxist theory, communism-as-a-system (communism-as-an-ideology is simply the ideology which seeks communism-as-a-system as its ultimate goal) is what happens to socialism (which uses the State) when it succeeds and the State withers away.
If the State hasn't withered away, you have (in Marxist parlance) socialism-as-a-system even if you have communism-as-an-ideology that motivates the present use of socialism-as-a-system. You can't have communism with a State.
(Whether you can have communism at all in practice is still an open question.)
By the way, just for kicks, here's a quote from Marx:
The contradiction between the vocation and the good intentions of the administration on the one hand and the means and powers at its disposal on the other cannot be eliminated by the state, except by abolishing itself; for the state is based on this contradiction. It is based on the contradiction between public and private life, between universal and particular interests. For this reason, the state must confine itself to formal, negative activities, since the scope of its own power comes to an end at the very point where civil life and work begin. Indeed, when we consider the consequences arising from the asocial nature of civil life, of private property, of trade, of industry, of the mutual plundering that goes on between the various groups in civil life, it becomes clear that the law of nature governing the administration is impotence. For, the fragmentation, the depravity, and the slavery of civil society is the natural foundation of the modern state, just as the civil society of slavery was the natural foundation of the state in antiquity. The existence of the state is inseparable from the existence of slavery.
Precisely.
> What about fascist and quasi-fascist states?
Fascism, communism, nazism, socialism, etc, are subsets of leftism/statism.