The USSR did not have real labor unions. It had organizations that pretended to be unions while being part of the state apparatus. Actual unions would have been the worst kind of enemy for the Communist Party: independent organizations that hold the same ideological position as the party while representing the interests of labor against it. The party could not tolerate such challeges to its legitimacy.

In a market economy, successful unions are powerful interest groups. They tend to have more influence on political parties than the other way around. Much like big businesses, but on a different subset of politicians.