That is just stupid.
That's an interesting point. And you are correcrt in a way. But I believe the actual target of Mark's author was the original disciples themselves, and more specifically, the Twelve, and only indirectly their followers. Mark seems to want to discredit the Twelve themselves.
By the time John was written, the target was the Jews in general -- and the Jewish communities that had sprung from the Jerusalem church -- the followers of the Twelve you mentioned.
Marks treatment of the Twelve has caused scholars to wonder what purpose his harshness served. As William Telford describes it, in Mark, the Twelve appear frail, confused, afraid, and human.* They show numerous failings, such as misunderstanding Jesus teachings, deserting him, falling asleep on guard duty, and seeking undeserved power and status. Additionally, Peter denies knowing Jesus three times, and Judas ultimately betrays him. Bart Ehrman describes Marks portrayal of the disciples in the following terms:
Marks treatment of the Twelve is so harsh in fact that the other synoptic writers, according to Ehrman**,felt it necessary to alter, omit, or otherwise tone down Marks treatment of them.
I think the reason for this, generally, was that at the time of Mark's writing the tension between the Jerusalem church and Pauline Christianity -- perhaps best displayed in Paul's account of his confrontation with Peter at Antioch -- was, as you noted, a very significant issue.
But by the time of John's writing, the dispersed Jerusalem church and the more Hellenistic churches were then in competition for apostolic authority. Churches founded by Paul were seeking to reinvent Peter and crew in their image and claim their authority -- something Mark's author couldn't do with the Jerusalem church being only so recently dispersed and probably some original followers still alive.
* Telford, William R., The Theology of the Gospel of Mark (Cambridge University Press, 1999), p. 131.
** Ehrman, Bart D., Peter, Paul, and Mary Magdalene: The Followers of Jesus in History and Legend (Oxford University Press, 2006), p. 225.