A balanced matrix organizational structure is an org structure where there is equal power sharing between the project manager and the functional manager. This org structure lies between the functional org structure and the projectized org structure.
The balanced matrix is mostly used in IT but it is used as a "transitional" org structure from one org structure (usually the functional) to another (usually the projectized), so it is always temporary, and not permanent.
The main advantage of a balanced matrix is that it allows smooth transition from one org structure to the other, without disturbing the day to day activity of the organization.
The main disadvantage is that it creates a power struggle between the functional manager and the project manager and it confuses the team members because of the ambiguity over the authority of the two roles (team members will have two bosses and both bosses will fight over the resources).
To answer your last question, since a company that adopts a balanced matrix org structure adopts it just to transition from the functional org structure to the projectized one, then yes, it is a good place for a project manager to work and thrive.