What are potential problems with having a staffing process in which vacancies are filled on a lottery basis from among job applicants, or on a first come-first hired basis among job applicants?
Such a staffing process would be disastrous for a firm. It would give the firm a staff that was likely to be incompetent, or at least much less competent than it should be.
The whole purpose of hiring is to get the right person for the right job to the greatest extent possible. The sort of random selection procedures described in this question would not achieve this aim. The people doing the hiring would not be able to evaluate the applicants and select the best one. Instead, they would essentially be gambling blindly.
A random hiring process would give a firm workers who were not necessarily any good at their jobs. This would make the firm much less efficient and profitable than it should be.