Unfortunately, if the media didn't have the royal wedding to fasten onto, it would just find something else equally trivial to replace it with--because the media itself is the problem, not the wedding. Likewise, people inclined to worship celebrities would just find someone else to fasten onto if the royal family weren't there.
As for the rest... What many Americans don't seem to grasp is that the monarch of Great Britain and her representatives throughout the British Commonwealth actually have a function: they perform the ceremonial duties of a head of state, such as greeting other heads of state, allowing the elected head of the executive branch of government to get on with the business of running the country instead of wasting time on diplomatic pageantry. In the States, you've conflated the two positions into one, but they are in fact separate responsibilities. So the money spent on maintaining the monarchy is actually a salary and expense account of sorts, not a sinecure. (The question of whether the diplomatic pageantry should be necessary is a separate one, but the fact remains that under current circumstances, it's required if a nation wants to function within the international community.)
In terms of authority, the British aristocracy is a joke (it was defanged for good when the House of Lords became an elected body) and most people living inside the Commonwealth know that. To put it another way: the members of the Queen's family have exactly as much authority of any kind as the latest manufactured pop star (and tend to handle what little they do have rather more gracefully). If you're going to be stuck with celebrities anyway (and I agree that these silly cults are a bad thing, but there seems to be no eradicating them), there are worse choices. ::shrug::