No, it would not be desirable to hire people in this way. While the match between the person and the organization is clearly important, the match between the person and the job is very important as well.
The match between the person being hired and the organization doing the hiring is clearly important. A person who is not a match for the organization will not fit in well with the culture of that organization. The person will, therefore, not do a very good job of working with others in the organization and will probably be less productive as a result.
However, just hiring a person who is compatible with the organization is not the answer either. A person must be a good match with the job in order to do well. If you hire a person who is absolutely perfect for your organization, it will not do you much good if that person is not qualified for the specific job and/or does not like that job.
Therefore, it is important to hire people who are compatible with both the organization and with the specific job.
The literature supports the idea that both person-job fit and person-organization fit are important in the hiring process. Edward (1991), for example, determined that a good fit between the job and the person filling it will result in lower stress, higher attendance rates, better retention, and better performance and job satisfaction. Edward conceived of person-job fit as defined by both demands-abilities (meaning that the person has the necessary knowledge, skills, and abilities to fill the job) and needs-supplies (meaning that the organization can meet the needs of the employee). A person must satisfy the demands of the job, and the organization must meet the needs of the person for the employee to experience job satisfaction.
In addition, a person must fit within the norms and culture of an organization. Chatman (1989) found that person-organization fit had a large effect on employee satisfaction. Person-organization fit is also important so that people can shift job responsibilities within the organization as the need arises and still find a fit with the culture. Therefore, both person-job fit and person-organization fit are important, and it would not be desirable to hire a person only according to the person-organization match.
Chatman, J.A. (1989). Improving interactional organizational research: A model of person-organization fit. The Academic of Management Review, 14(3), 333-349.
Edwards, J. R. (1991). Person-job fit: A conceptual integration, literature review, and methodological critique. In C. L. Cooper & I. T. Robertson (Eds.), International review of industrial and organizational psychology (vol. 6, pp. 283-357). New York: Wiley.