Some departments in US STEM universities require the applicant to mention the names of faculty members with whom they are interested in working with within the online Ph.D. application system. So do the faculty members, whose names are not mentioned in the online system, not review these applicants?
What you describe might happen, but would be rare. Probably very rare. Doctoral applications in the US are normally handled by a committee on which faculty will serve for a few years. But every system is different.
The request for names is more likely to be the case of wanting to get a sense of the load on faculty that would be required overall by an applicant pool. Another reason might be to induce applicants to learn something about the faculty of the department before they apply.
There are a few fields (lab science most likely) where a student needs to join a specific lab and may even be funded by grants held by that lab. In that case a different system might be used.
But in most fields/universities admission is a departmental matter, not controlled by individual professors.
See the answer for the US to this question: How does the admissions process work for Ph.D. programs in Country X?