St. Paul was superior to bishops; he appointed them.
... one is unqualified to be a bishop unless he's demonstrated the ability to control his own kids.
So, not only are celibate men ineligible to be bishops, but married men who are childless are also ineligible? Where does that leave Jesus (unmarried, no natural children)? Where does that leave men who take the Biblical command "Imitate me as I imitate Christ" (1 Core 11:1) literally, including obeying Jesus' words in e.g., Mark 10:29 or Luke 18:29?
Historically, the verse you cite has never been interpreted to prohibit the ordination of celibate or childless men to the episcopacy. It is true that married men were ordained in the early church. (A church consisting primarily of adult converts from paganism, of course.) St. Paul is setting limits on the sort of married men who can be ordained (married only once, with Godly children if any), not prohibiting the ordination of celibate or childless men.
Indeed, Paul was an apostle.
So, not only are celibate men ineligible to be bishops, but married men who are childless are also ineligible?
That's certainly the prima facie reading of it.
Where does that leave Jesus (unmarried, no natural children)?
Unqualified to serve as a bishop, in any conventional sense.
Where does that leave men who take the Biblical command "Imitate me as I imitate Christ" (1 Core 11:1) literally, including obeying Jesus' words in e.g., Mark 10:29 or Luke 18:29?
The same. It's not as though the inability to serve in a particular role is somehow crippling, or evidence of spiritual unfitness. I assume you'd agree that a woman cannot be a bishop, but that hardly reflects badly on her or proves that it's an unreasonable criterion.