Your argument presupposes that an objective criteria is optimal. It's trivial to refute that, for example a company could hire people based on whether they are greater than 6 ft tall, that's an objective criteria but it would still be terrible.
Objective doesn't mean "good/optimal/solved" and subjective doesn't mean "bad/suboptimal/unsolved". All subjective/objective refer to is how sensitive a property is to a specific context. An objective measure is not particularly context sensitive whereas a subjective measure is.
My company has both objective and subjective criteria. Competency is mostly measured objectively and represents the bulk of our hiring criteria, the subjective assessment involves things like communication, collaboration and professionalism.
Both aspects are difficult and imperfect to assess regardless of whether they are objective or subjective, but I don't think it's particularly appropriate to assess someone's competency based on a subjective measure.
If someone is a good basketball player, or a good plumber etc... they are likely good regardless of the intricacies of the individual making the assessment that day and hence it's something that is probably best measured objectively. However, whether someone will get along with the rest of the basketball team, or whether a plumber can properly communicate to a customer what the issue is and how to fix it, that may very well depend on what team that player is playing for, or the relationship between that specific plumber and the specific customer. That would be more of a subjective criteria.
There certainly are subjective aspects to competency as well as objective aspects to communication, but it's minor (perhaps a basketball player is good only on a specific team, perhaps a plumber is illiterate).