The monarch and consort are anointed by the church. In the eyes of the CoE, Camilla and Charles are not married owing to the fact that Camilla's ex-husband is still alive. The CoE doesn't recognize divorce, so therefore the two could not be married within the Church. If you then continue this logic, a woman who is not married to the king in the eyes of the Church cannot be crowned as the king's consort by said Church. In not crowning Camilla as Queen Consort they can establish a precedence - a monarch can divorce and remarry, or marry a divorced woman (or man), but if the marriage cannot take place in the church then the spouse doesn't get the big title. Thus, Camilla doesn't become a Queen owing to her first marriage, while Catherine does owing to her lack of a divorce.
Where it gets tricky is that there have been previous monarchs and consorts who have had multiple marriages - notably Eleanor of Aquitaine and Henry VIII - but as both had their marriages recognized by the church, the coronation becomes justified. Charles and Camilla have been blessed by the Church, but the Church itself still has the official divorce is a no-no stance.
I do agree with this completely. I don't want to see a regency set up simply because HM is old, I don't want to see Camilla be denied the Queen consort because of her divorce/Diana, I don't want to see Charles become George VII simply because of the Young Pretender... doesn't mean it won't necessarily happen.