(Arthur Drews, Witnesses to the historicity of Jesus Christ)Indeed, even the suffering servant of God in Isaiah was so unmistakably described as man that the most resolute elevation of his figure to the supernatural and metaphysical world, such as we find in Paul, could not obliterate his human features. The question is, whether these features are those of a real, that is to say historical, man: whether the heavenly being which must appear as a man according to Paul came upon the earth at a definite moment in historyIndeed, even the suffering servant of God in Isaiah was so unmistakably described as man that the most resolute elevation of his figure to the supernatural and metaphysical world, such as we find in Paul, could not obliterate his human features. The question is, whether these features are those of a real, that is to say historical, man: whether the heavenly being which must appear as a man according to Paul came upon the earth at a definite moment in history.
Surely the Ignatius et alia's emphasis that Jesus died "under Pontius Pilate" betrayes all the desire of placing the Paul's Jesus "at a definite moment in history", but Paul never specifies which is the "right time" for Jesus's death. If that time was more specific and/or recent in the eyes of Paul, why wasn't he more specific?
If you say, á la Maurice Casey, that it's idiotic (I go to memory) for Paul remember that Jesus was crucified by Pilate, then why did Ignatius insist so much to remember that Jesus was crucified "under Pilate"? Evidently it was theologically necessary for Ignatius remember Pilate. Why couldn't it be as well theologically necessary for Paul? Only because the enemies of Paul weren't the same enemies of Ignatius? In both the cases, you are moved to accept
1) that Paul didn't know no Pilate, and so no historical Jesus, (since he never mentions Pilate)
Or
2) that the enemies of Ignatius didn't know no Pilate, and so no historical Jesus (since Ignatius takes disturb to remember them the role of Pilate)..
In both the cases, you have to admit the existence of mythicist Christians.
A possible objection represented by the claim that the enemies of Ignatius were only docetic historicist Christians and not docetic myticist Christians is easily confuted: if the enemies of Ignatius were docetic historicist Christians, then Ignatius would have simply need to remember that "Jesus really suffered and died". The addition of Pilate continues to be not-necessary for a simply anti-docetic Ignatius...
(just as mentioning Pilate would be not-necessary for a presumed historicist Paul)
...unless the enemies of Ignatius were docetic mythicist Christians, i.e. Christians who didn't put the apparent crucifixion of Jesus "at a definite time of history".
And as for the enemies of Ignatius, so for Paul.
So the more simple explanation is that both Paul and the enemies of Ignatius didn't put Jesus's death under Pilate.