This legislation is about as well named as the Patriot Act.
How do I have more freedom to join a union or not by being exposed to pressure to sign (or not sign) a card? If I sign that card, my "evil employer" may discover that I did, and act against me. Or I may be pressured by union organizers and have to put up with that pressure and acts against me.
Secret ballot, just like we have for elections, avoids all this, because no one knows how I voted.
Or do you suggest that we start voting for president by have people run around and pressure me to vote one way or another?
Not a good idea. If unions are that great, then a secret ballot will let workers choose a union. If not, then, workers won't be forced to show whether or not they support a union, and will avoid any acts against them by anyone.