no He didn't, He gave the keys to the kingdom of Heaven to Peter to proclaim that he would be titular head of His church after He had left the Earth....we all have the promise of Heaven, but we certainly don't have the keys and far too many of us refuse the heavenly gift and choose to disobey the rules and live lives that are not acceptable to God.....no Heaven there
I guess that explains all the jokes that begin with, "A guy died and St. Peter met him at the pearly gates of heaven...". ;o)
In truth, though, Jesus gave ALL His disciples the "keys to the kingdom of heaven" which is the gospel. See John 20:21-23, and not just the one passage in Matthew that is misinterpreted to single out Peter only as the holder of the keys. Keys OPEN doors - Jesus IS the door to the sheepfold - and the gospel is the way that souls are admitted into it. That is also why the "gates of hell/hades" would not prevail. The gospel is the key to those gates, as well, and all who come to Christ will be delivered.
So, yes, we ALL also have those keys, as we minster together to proclaim the saving truth of salvation by grace through faith in Jesus Christ, who died for our sins and was raised for our justification. The only succession spoken of in Scripture is one of a handing down of the "rule of faith" and not a special office called "Apostle". THAT one had very specific qualifiers and is why there are no more living Apostles today. Christ is the head of the church and he will never fail us. As Christians, we have the SAME Holy Spirit that Jesus breathed on his disciples and we, also, are given the ministry of reconciling the world to God through the gospel.