To me the key aspect of this issue is the question of who should decide whether the Queen (or any other UK monarch) should abdicate. What would be the position if the people and/or Government thought she should abdicate, and she didn't want to; or vice versa - she wanted to step down, and we didn't want her to? I think the reason the Queen has just more or less stated that she doesn't intend to abdicate is that if it was perceived that abdication was in response to popular or Government pressure, then it would be a first tentative step towards a democratically chosen/elected Head of State.