The US is closed shop, by law, Actually, Closed Shop (by its standard definition , meaning only union members may work) is illegal, but the problem you describ

The US is closed shop, by law, Actually, Closed Shop (by its standard definition , meaning only union members may work) is illegal, but the problem you describe is real enough. Agency Shop (typical except in right-to-work states) is effectively closed for new employees. There are workplaces where different roles have different unions, like CNA and SEIU in certain CA hospitals.