"Ends of the earth" is a spatial reference, not a temporal reference. It refers to geographical limits, not the terminus of the age(s).
How could the original apostles do it without successors?
And Matt 28:19 says until the end of the world
Jesus Christ extends his mission, power, and authority to His church of His apostles! The apostles have the same mission, ministry, power, and authority as Christ! Jn 20:21 as the father sent me, so I send you!
Even His judging!
Matt 19:28 and 1 cor 6:2
His teaching authority!
Matt 28:19 and Jn 20:21
His power to forgive sins!
His being the light of the world!
His ministry of reconciliation!
2 cor 5:18
His authority in governing the church and administering the kingdom!
Matt 16:18-19 & 18:18 Jn 21:17
Apart from me you can do nothing. Jn 15:5
Acts 2:42 doctrine of the apostles!
So the church is subject to Christ!
Christ shares His glory! 2 thes 1:10 rev 12:1
The pillar and foundation of TRUTH!
1 Tim 3:15
The TWO EDGE SWORD!
To proclaim the truth! Matt 28:19
To condemn error! 1 cor 16:22
Jesus Christ founded the new covenant church for the salvation of all men! (Jn 1:16-17) Christ is the truth! (Jn 14:6) Christ and his church are one!
(Acts 9;4 Jn 15:1 eph 5:32)
The church is the pillar of truth
(1 Tim 3:15) that must teach all men (Matt 28:19) without error guided by the Holy Spirit
(Jn 16:13) Thru the grace of God in the sanctification of souls applied in the seven sacraments!
Jesus Christ continues HIS ministry in His new covenant church thru Peter, the apostles, and their successors with the same mission, power, and authority!
Mt 16:18 Mt 28:19 Matt 18:17 Acts 1:17 acts 8:31 & 35 acts 9:4 Lk 10:16 Jn 8:32 Jn 13:20 Jn 15:5 Jn 16:13 Jn 20:21-22 eph 2:20 acts 2:42
1 Tim 3:15
unto all time and all place