In the aftermath of the resurrection of Jesus and the death of Judas at his own hand, the Church seemed poised to do nothing but await the fulfillment of the promise of the Lord for the coming of the Spirit. But in fact the Church was not idle during that time. Under the guidance of the Spirit, the apostles gathered to fill in their number and replace Judas. In the Acts of the Apostles, St. Peter not only discusses who should replace Judas but lays out a set of criteria for the one who would replace him. The apostles did not presume to know the one whom God had in mind but they did know that whoever was to replace Judas had to be one of them, one of them from the beginning of Christ's public ministry, and one of them who was not simply a follower from afar but close to the Lord and to them. St. Peter them laid out that criteria before naming names and once the qualifications had been laid down, and only then, did the apostles pray to God for guidance, and ultimately Matthias was chosen.
We have, of course, the qualifications laid down by St. Paul in his letters to Timothy and Titus. These are certainly determinative for those who would presume to serve as a pastor or deacon or bishop of the Church. However, these are not solely determinative. In other words, nothing prevents the Church from further narrowing the list and setting up requirements in addition to what St. Paul has laid down. It was in this realm that the Church developed a seminary and laid out a curriculum as well as an internship that became the minimum requirement of those who serve God's people in His name.
Some churches have abandoned St. Paul's list. It is no secret that many churches no longer ordain only men and have allowed those who live in conflict with the Biblical model of marriage (one man and one woman). But it is also true that in this day and age many have raised questions about whether or not the churches are asking too much and narrowing too small the numbers of those whom they will ordain. The advent of online education and the growing need for pastors to replace the boomer heavy ministerial rosters of most churches. My own church body has moved in this direction. Residential seminary education is now one, perhaps the primary, but still only one of the options available to those who seek to serve as a pastor. What is interesting is that while Missouri and others are looking to relax requirements, the Roman Catholic Church has added to the requirements and lengthened the time of preparation.
In the end it should be noted that no one has a right to serve as a pastor or is owed a place in the ministerium. It is well within the Church's perogative to add to St. Paul's list. It is also worth noting that the Scriptures warn against laying hands too quickly on a convert. The needs of the churches are not best served by eliminating the criteria but by making sure that the best and the right men are set apart by Word and prayer and the laying on of hands to stand in persona Christi in delivering God's Word and Sacraments to His people.