The idea of having individual employees choose which union they want sounds a lot like the idea that consumer choice drives change (which usually does not work except in the case of huge boycotts, which are limited in their effects). Unions are about democracy in the workplace. If everyone is in a different union, there can be no legitimate democratic decisions on behalf of the workers.

EDIT: There's a bit of an exception. For example, in universities, sometimes graduate students have a union and faculty have a union. It doesn't make sense to place them both in the same union because the faculty boss graduate students around. However, it would make sense for the two unions to cooperate against the administration.

EDIT2: Another reason unions should be as concentrated as possible is so they form a united front against the bosses. If every employee is in a different union, how can they achieve anything without great difficulty?