Since Paul's understanding of the purpose of Moses' veil differs from that of the version in Exodus, we are prompted to wonder why. Boring & Craddock, in their New Testament Commentary, suggest that Paul thought that the veil like other components of Jewish religious faith were not necessary for Christians.
For Paul, none of us need to be protected from a view of the glory of the Lord. The New Interpreter's Study Bible suggests that Paul may be referring to the new covenant as described by Jeremiah, "No longer shall they teach one another, or say to each other, 'Know the Lord.' for they shall all know me...." (Jeremiah 31:31-34).
When we try to get a modern meaning from an ancient text, we really ought to spend some effort on thinking about what the text meant when it was written--in this case: what was the underlying problem that Paul was addressing.
Allen & Williamson, in Preaching the Letters are helpful. Paul is trying to overcome the problems he believes that the super apostles have caused in Corinth. He is rebutting claims that they have made about him:
....The other missionaries have incorrectly used Exodus 34:29-34. Paul speaks with great boldness, that is, not viewed but frankly and publicly. The super apostles imitate Moses, but not in the way they think they do. According to Paul, they speak from behind a veil, preventing the community "from gazing at the end of the glory." In other words, they prevent the congregation from seeing clearly the nature of the coming realm of God beside which the glory so prized by the super apostles will fail. Therefore, the super apostles and those who follow them are "hardened against the purposes of God in the same way as Pharaoh."