Yes, the monarch is much more of a figurehead these days but she is there to create stability. Britain (as well New Zealand) doesn't have a constitution, and, from what I understand, this means that they need a monarch or it leaves them open to abuses of the system. I believe that if there was a serious problem with the British (or NZ!) Government such as a coup, a revolution or fascist attempts to remove basic rights from British citizens, then she could step in. I would say that the military have to swear allegiance to her, so technically in extreme cirmcumstances she could command them to act as she sees fit. Of course, these aren't very likely to happen but she must be acknowledged as a back up plan. I think other countries imitate this system by having both a prime minister and a president (the equivalent of a monarch).That being said, however, the monarchy is a figurehead; sure the crown TECHNICALLY has the power to veto anything... but there'd be riots if she did, and she's never done so before.
The throne is a cultural thing at this point, and by cultural, it is also traditional, and tradition is that the throne is passed when the holder dies.
Even so, charles, although not nearly as popular, is really not that bad a guy, from whot I've actually read up upon him about, he's actually pretty good with money and such, which would probably help alot of the palace's issues with finances.
I've no clue about camilla though.
Then again I could be misinformed about all this...
And as for Charles being more frugal, I don't think he's anything impressive money-wise. Have you heard about his boiled egg thing? Seriously weird! And the Queen is known to be obsessed with frugality. She won't let the Palace footmen walk on the hallway carpets in order to better preserve them for longer.