The requirement is to be called by Jesus and follow Him. Paul was personally called by Jesus. Matthias was not.
Matthias did not take the Heavenly office of Judas, but the Earthy.
There are 2 verses to contemplate. Matthew 19:28 "you who have followed me". There is an important prerequisite: the personal calling must be first. Judas was called, but did not follow. This does not exclude Paul, but specifically includes Paul. Paul was called by Jesus and he did follow.
Luke 22: 28-30. Here Jesus is talking to the 11 who stayed with Him. Judas is excluded from this promise. Matthias couldn't take Judas' throne because Judas never had a throne.
The seat on the thrones are Jesus' to give. He who sits on the throne must be personally called by Jesus and that person must follow Jesus. Jesus called 13, but only 12 followed. Jesus never called Matthias to follow. Jesus did call Paul.
****The requirement is to be called by Jesus and follow Him. Paul was personally called by Jesus. Matthias was not.
Matthias did not take the Heavenly office of Judas, but the Earthy. ****
Did the Apostles choose the wrong person? If they had they would have been out of the weill of God and the Holy Spirit would not have fallen upon them.