Do we need a meddling Monarch?

Memos from Prince Charles to UK Ministers (published by the Guardian after a decade-long legal battle) reveal that the next-in-line-to-the-throne may not take the impartial, non-political approach characteristic of his mother, Queen Elizabeth. The memos reveal that Charles is quite prepared to intervene in matters ranging from badger-culling to heritage preservation to agricultural regulations.
One of the memos directly involves New Zealand. Writing in 2005 to Tessa Jowell, then UK Secretary of State for Culture, about the conservation of the Shackleton and Scott Huts in Antarctica, our future King recalls a conversation he had with Helen Clark. Although Jowell's department is, he believes, unable to assist projects "overseas", he wonders whether Antarctica isn't somehow "British" and hence not technically "overseas", and he asks her, even if it's "futile", to apply "a bit of imaginative flexibility in the interpretation of these rules."
He may be well intentioned. After all, the preservation of the Shackleton and Scott huts is a worthy cause. But, here we see the future monarch using his personal influence for a pet project and asking a minister to bend the rules in its favour. It appears that anyone able to influence him could well be able to influence public policy by pulling strings at the highest levels of government.
The most eye-popping of the memos is the one to the PM, then Tony Blair, in which the Prince attempted to influence the UK's agricultural policies in ways that would have contravened UK and EU regulations.
The UK's monarch is equally New Zealand's monarch. Queen Elizabeth has set a good precedent of impartiality, allowing the democratically elected government of the day to get on with its business. She has a right to be privately informed and advised by, and to warn, her ministers. But she does not meddle in government either in the UK or in her other realms, such as New Zealand. Her role (and the role of her appointed Governor-General) is constitutional, not political. After all, the monarch is not elected. Once the Sovereign begins to get involved in politics and public policy, then he or she could become a target for lobbying.
The publication of these memos is a major embarrassment for Prince Charles, and they bring into question his suitability as monarch. In fact, they bring into question the suitability of New Zealand's retaining the British monarch as its head of state at all. There is no reason in principle why Charles, as future King, would not seek to use his private influence over ministers in New Zealand in order to see to it that his pet projects were treated with special favour. Do we really need that?