All that is required is private ownership;

Defining it that way is simply ahistorical. If we look at capitalism historically, it does seem to be intrinsically tied to wage labor. It's only once we abandon a historical look at capitalism that we can abstractly say that, "Well, it could have wage labor." But it's a historically specific mode of production, and a part of that is wage labor.

Isn't it funny that Marx died without ever defining what a class was?

...Class is one of the best defined things in marxist theory. Here's a good overview of the marxist definition of class. To quote it:

[Class is a] group of people sharing common relations to labor and the means of production.

That's a nice, simple, and concise definition of class.

The state offers an avenue for corps to gain privileges under the law, which allows large corps to use law to stave off competition from smaller and medium size corporations.

So? That's been present since the start of capitalism. None of that is at all anti-thetical to the features of capitalism.

If your prefered system solves any of these problems in the real world, then why the fuck can't you guys get it to work ANYWHERE in the world?

Because modes of production are all encompassing, and the tendency of capitalism is to expansion, so, to get anything post-capitalist to work, we'd need global revolution, or else we'll get crushed and never actually move beyond capitalism.

It's been tried soooo maanny times and places and cultures.

Not really. At most, I'd say the soviets in Russia that formed in 1905 were working toward socialism, fighting a social revolution against the Russian state, until they finally got crushed by the Bolshevik counter-revolution in 1917 (or 1921 for the free soviets in Ukraine), the briefly lived räte in Germany in 1918 did similarly, Turin, Italy in 1919 to 1920, France in 1968, and a handful of others. That's not "sooooo maaaaannny times". I mean, as modes of production go, capitalism isn't very old, only being, like, half as old as feudalism was when capitalism finally overtook it, so we wouldn't necessarily expect for capitalism to be overthrown by now.