Yes, that's the simplified happy ending for voting in a union but the reality is complicated by factors outside of the union's control.
E.g. A $15/hour worker considering a union weighs the possibilities: a raise of wages to $20/hour or a reduction to $0/hour because there are no jobs at all.
That's the complicated calculation. Union representation can negotiate a Collective Bargaining Agreement to raise wages but a union can't guarantee the existence of the jobs[1] to pay those wages. Many employees know this which is why they reject unions. UAW has tried to unionize workers at Toyota in Kentucky for decades and failed. Nissan workers in Mississippi just rejected a union vote last month. FedEx Freight drivers in North Carolina and Pennsylvania recently voted and decertified their union in July 2017 after voting for it in 2014.
Some workers genuinely feel a union will make their economic lives worse. The unions' promises of better wages mean nothing if the plant closes and workers weigh that possibility when rejecting union representation. What arguments do we use to convince these people that they haven't already heard from pro-union organizers?
[1] examples:
Seattle union can't stop Boeing from locating the new 787 Dreamliner factory in South Carolina with no unions.
Steelworkers union in Indianapolis doesn't stop Rexnard from eliminating $25/hour jobs which cost more than $3/hour jobs in Mexico.
Nabisco (Oreo cookies, etc) moves production to Mexico instead of keeping the higher wage union jobs in Chicago.
The common theme is that the fear of no jobs is not FUD nor a theoretical threat. Workers know it actually happens.