To be an Apostle, you had to see the Risen Christ and to be able to perform signs and wonders.
Actually not quite -- read Acts 1, where exactly is that stated that Matthias HAD to see the Risen Christ to be chosen?
But more to the point, the successors of the Apostles are not the Apostles themselves, but their disciples to whom the authority i.e. the burden of maintaining the true faith was handed down.
What is this? It is just the holding true to what was taught to them and to their teachers, all the way back to Jesus Christ.
The verses I cited point out clearly how Jesus gave the apostles authority as in Matt 16:19 and 18:18 18Verily I say unto you, Whatsoever ye shall bind on earth shall be bound in heaven: and whatsoever ye shall loose on earth shall be loosed in heaven
you can see succession in Acts 1:20 his bishoprick let another take -- this was the clear way for Early Christians to know that they were taught the Truth -- as we read in 2 Tim 2:2 this is to be handed down from teacher to taught
What is the point of this? For ensuring that the Truth was taught and not diverted as we see among Jehovah's Witnesses or others.