Yes, o.k.
I re-read some of Edersheim's great work, the Life and times of Jesus the Messiah and he agrees with you to a point that I am willing to agree with as well.
The gist of it all is, though, that Christ was going away, and He was leaving the work of the church that He had established, to the apostles and to the disciples. Later in Matthew 18, he addresses all of them with the same concerns.
Peter did preach to the centurion and he did have the vision about the animals that opened up the church to the Gentiles.
Still, He gave all of them the keys to the kingdom, and as we know, the kingdom is spiritual and the kingdom is within, and so these have to be spiritual keys. Making disciples and guiding those disciples in a Christian life, and in establishing church procedures were all included in the stewardship. Peter was one pillar, there are 12 others.
Edersheim also says that "loosing" and "binding" refers to things that are prohibited and permitted. In Rabbinic law the terms could refer to pardoning and forgiving but this is not the case with Christ, and forgiveness of sins is not to be considered the meaning