No individual worker can hold enough shares to matter. Unless you're talking about a labor union buying a non-trivial stake in an employer? I've never heard such an idea before, but I'm sure at someone else has thought of it in the past I would be curious to see how that went. It also doesn't do anything at a private company.

In the US? Sure. If a group thinks specific representation will make "things" better for their group, then this is a method occasionally exercised.

In certain circumstances, a judge can also appoint you to a board, or even to a CEO position (been there, done that) - but things are generally fairly broken if that happens.

Wouldn't that rely on the workers having enough money in the first place to do that? Ignoring the issue of non-public companies.

If workers had enough capital to do that they'd be capitalists not workers?

Why don't the poor just buy money? Seems logical enough to me.