Technically, if a CEO is on the board, then a company’s employee is on the board. Shareholders will probably not vote to put a line level employee on the board, though.
The compliment to "workers aspiring to join the owning class" is that the biggest risk a capitalist faces is the possibility of being thrust back into the working-class, and having to actually work for a living, as opposed to living off of profits derived from the labor of others.
In practice, socialism is a power grab where populist leaders redistribute the ownership classes' assets to themselves.
Wikipedia's treatment is a bit more nuanced. https://en.wikipedia.org/wiki/Socialism
Is this how workers’ councils work in Germany?
So the conversation becomes, should the government(s) in the US force businesses to place line level employees on the board (if the line level employees want to be on the board), and under what parameters?
In Germany, they do find it economically viable and important for line level employees to have direct representation on the company board. Talking about the CEO or other management classes being on the board is missing the conversation. Suggesting that because US companies don't believe in the economic value is missing the conversation. Suggesting that people are saying that this type of board composition is illegal is also missing the conversation. No one said it's illegal, but it's equally not a legal requirement either like it is in other places.
The conversation is that this composition doesn't exist, by and large, in the US, and people think it should. People seem to believe that it does have value to the business.
So yes, it does seem like you're creating semantic arguments because your points miss the conversation semantically.
On the other hand, we do have higher productivity, but not having codetermination probably isn't the reason for that.