Unions can definitely influence them. E.g., that's a big part of the point of the German Betriebsrat: https://en.wikipedia.org/wiki/Works_council#Germany

Unions can influence them only while they're in CBA negotiations unless they negotiate a seat at the table, as in your example, which is not something that is at all common in the US.

Formally, that's true. But as we see in the writer's strike, unions definitely try to influence business decisions, and sometimes they succeed.