the only difference being that whereas communism and socialism openly call for state ownership of all property
Socialism and communism don't advocate for state ownership of all property. They advocate for common ownership of the means of production. Common ownership doesn't have to be state ownership, cooperatives are for example another form of common ownership. They certainly do not advocate the state should own all property, even in the USSR private property existed.
The far left comprises the pure forms of all the rights-violating social systems: communism, socialism, fascism, Islamism, theocracy, and anarchism (i.e., rule by gangs).
Okay so you basically make a personal definition of far left as anything you personally don't like, that doesn't really leave anyone more clever on anything or provide an argument for anything
If anything is a rule of gangs it's capitalism. A tiny, rich elite wields power over the economy, if the government or people do anything they don't like, they can move out or try to sabotage the economy. They can funnel immense amounts of money into campaigns and lobbyism to exert far more influence than an ordinary worker. Not only do they dictate politics in many countries, but in workplaces too capitalists can rule like gangs to reap most of the value created by the workers for themselves.
The far right comprises the pure forms of rights-respecting social systems: laissez-faire capitalism, classical liberalism, constitutional republicanism. All of which require essentially the same thing: a government that protects and does not violate rights.
A government that protects the "rights" of a rich elite to siphon wealth off the working masses but doesn't care for the homeless, people born into poverty, people being unfortunate to catch diseases or workers spending 60 days a week and making 1/1000 of a landlord or capitalist. That's not a notion of rights that even makes any sense.
I pay 40% in taxes but I have more than enough to eat, wear and stuff, as a finished master student I was used to an income less than 1/4 of what I make now, would I feel my rights are violated if I paid 50% to make sure there were cheap public housing being built for the working class? 55% so future students could have a decent stipend? 60% to make sure nobody had to be homeless? No, I would say our rights would be improved and be happy nobody should fear such a fate. Would I be less incentivized to work? No, fortunately I find passion in it (I can understand those who don't) but I see it as everyone's duty to contribute according to their ability. However I would definitely feel everyone's rights would have been violated if taxes were cut and I had to buy my own health insurance... Knowing all the poor people who then may not afford it and knowing it would probably be even more expensive and less efficient (compare USA's health costs to other western countries... no thanks!)