tl;dr: Everything you just typed out was wrong.

No, states cannot exist under Communism. Communism is a classless, stateless, moneyless, post-scarcity socioeconomic system without any contradictions inherent to itself. Chiefly, it is organized along the lines of "From each according to their ability...". Those nations that you listed do not, or in the case of the USSR did not, claim to have achieved Communism. No nation has ever achieved Communism. The closest thing the world has ever seen to Communism was primitive Communism in pre-agrarian societies.

Socialism is, by no means, the "friendlier variant" of Capitalism. You may be confusing Socialism with a Social Democracy, which is the system that the Nordic countries operate under and is the ideology of one Bernie Sanders. The nations that you listed have/had never achieved Socialism either. Socialism a.k.a lower phase Communism, can be characterized by 6 main things:

1. The complete abolition of capital (moneyless)
2. The complete abolition of classes (classless)
3. The complete abolition of wage labor
4. The state has become a vestigial organ of society and begins to wither away (stateless)
5. The complete abolition of the world market (global dominance, Socialism & Communism are global ordeals and cannot be achieved in one area or nation)
6. The mode of distribution is a worker planned economy

What the nations you listed have/had achieved is known as the Dictatorship of the Proletariat. I know dictatorship might be a scary word to you, but all that means is the political and economic domination of the proletariat class. It doesn't mean an actual dictatorship. Right now, assuming you don't live in one of the nations that you listed, you live under a Dictatorship of the Bourgeoise, because you live under the political and economic domination of the bourgeoise class. A Dictatorship of the Proletariat isn't as simple as Socialism, and CAN be characterized by (though not necessarily all) 8 things:

1. The ongoing abolition and suppression of capital
2. The workers seize the means of production and the MOP are owned by the worker directly or indirectly via the state under a principled Communist party
3. The ongoing abolition of wage labor
4. Bourgeois state is smashed and replaced with self-organized workers (with guns! the worker's state)
5. The ongoing abolition of classes
6. The ongoing abolition of the world market
7. Acts as a transformational period between Capitalism and Communism
8. No strict distinguished mode of production, can look like many different things

All nations that have a DOTP should be supported by all self-prorupted Communists. End sentence. I don't care what you heard from your CIA-approved news source about the PRC genociding Muslims or terrorizing innocent Hong Kong protestors. The reason that the nations you listed that are still around today have limited private property is for survival purposes only (DPRK doesn't by the way). When the USSR was illegally dissolved in 1991, the nations that were supported by the USSR had 2 choices: market reforms, or death by sanction. To not open up and allow some level or private property would have resulted in the deaths of COUNTLESS in Cuba, Vietnam, and Laos. This was the cause of a famine in the 90's in the DPRK.

The state is a necessity in achieving Communism, lest we let the power of the bourgeois state crush our Socialist projects with the snap of its fingers. The state holds a monopoly on political violence and repression, which in a Capital-dominated nation are used against Socialist projects on a day-to-day basis. We, as principled Communists, take the state, flip it upside down by establishing a DOTP, and repress the bourgeoise class out of existence. By the way, Anarchists want states too - you special folks just like to call it by different names. I don't care how libertarian and horizontal your democratic militia fighting force is, it's still an appendage of whatever democratic system your running your commune under. Democracy is incompatible with Anarchism, Democracy requires a state. Those labor camps that the CNT-FAI used to imprison fascists were totally stateless and nonhierarchical, right? The political repression of the Bolsheviks under the bandit king Makhno was totally stateless and democratic, right? No. Wrong. The only difference is, in our state the hierarchy is official and accountable, yours is not.

In conclusion, reject your Anarchistic idealism, read State and Rev by Lenin, embrace Marxism. Ask me questions if you want I'll probably answer them. Bye.