i.e. They had the choice not to respond or to have a aide respond, but the prime minister chose to respond.
Would you suggest that someone in the monarchy shouldn't express an opinion for fear that the receiver of the letter will pay too much attention to it?
Yes. That's absolutely the point.
Even strong monarchists promote this point [1], but conservative newspapers have (relatively recently) questioned the reality [2].
Until we can vote for the head of state, their opinions on all matters must not influence the government in any way.
[1] http://royalcentral.co.uk/blogs/insight/the-queen-is-the-per...
[2] http://www.telegraph.co.uk/news/uknews/queen-elizabeth-II/11...
My understanding is the monarch must not become actively involved in government... thus declining to vote, staying out of European Parliament, etc. That's not quite the same thing as never expressing an opinion.
But Prince Charles isn't the head of state... So assuming that you're suggesting that this principle doesn't just apply to the head of state, where do you cut the line? Should everyone in the royal family be barred from expressing their opinion privately or publicly?