But that is not the sense in which the NT writers used for the word *apostle*.
Acts 1:21-22 So one of the men who have accompanied us during all the time that the Lord Jesus went in and out among us, beginning from the baptism of John until the day when he was taken up from us—one of these men must become with us a witness to his resurrection.”
Nobody on the earth today can fit that qualification.
What qualification? “become one with us”? That’s not defining themselves as anything. We should all be apostles—witnesses to His resurrection by His presence in our lives.
My belief is that you are correct. An Apostle of the variety you speak has to have been personally called by Jesus, chosen by Him, followed Him personally, taught directly by Him, and sent by Him to preach the gospel to initiate the process of making more disciples. A succession of disciple-taught disciples, yes! A succession of Christ-taught Apostles, no!