Does 1 Corinthians 12:28 and Ephesians 4:11-12 imply that the church should be led by apostles only? What bearing do these scriptures have on the church today and it’s leadership?
To be honest, I do not see where you could get the idea that the church should be led by apostles only from the scriptures you use. I Corinthians 12:28 gives a list of several categories. However, this is not a list of leaders at all. It is a list of types of miraculous gifts/ministries. The context of this passage has nothing to do with leadership, so it is not really relevant to who should be leading the church. In any case, this passage lists a number of roles. It certainly does not focus only on apostleship.
On the other hand, Ephesians 4:11-12 definitely IS a list of leadership roles. It IS relevant to your question. This list includes several leadership roles, including prophets, evangelists, “pastors” (ie elders/shepherds) and teachers. With the passing of the apostleship and of inspired prophets, the leadership of the church naturally fell to the evangelists, shepherd/elders and teachers. We know from early church writings and also from later New Testament books such as 1 Timothy and Titus that this is what happened. With the passing of the apostles, the churches were led principally by evangelists and elders. Paul told Titus to appoint elders in every city in Crete(Titus 1:5). Obviously, there were no apostles in Crete, so the leadership fell to the elders/overseers, as well as evangelists such as Titus who appointed such elders. I Timothy describes the qualities required of elders and also mentions another leadership role–that of the deacon–in 1 Timothy 3:8-13. Paul met with the leaders of the churches in Asia, as described in Acts 20. These leaders were shepherds, not apostles. Peter appealed to the leaders of the churches in 1 Peter 5:1-4. Again, these church leaders are not apostles but are elders. He equates elder with overseer and with shepherd in this passage.
The conclusion is that God did not leave the Church leaderless with the passing of the apostles. In fact, through Paul and the other apostles, he provided a clear line of leadership through evangelists, elders, teachers and deacons. God took care of the need for leadership in Jesus’ church with the passing of the apostles.