Intra-union competition is a thing as is the ability for the company to not sign a contract. What they often lose out on is the ability to retain the previous union employees and with it lose all their training, institutional knowledge etc.
A company does not have to sign a union contract but those losses are part of the leverage unions use to balance the power structure
The whole point of a union is to eliminate competition on the labor side and ensure a given company is cornered into accepting the union’s conditions.