In short, a lot of us think the Queen is the least worse option, and regrettably accept, if not support the monarchy.
Speaking as an outsider, it seems to me that the main advantage of the modern monarchy is that it serves to represent the nation apart from the transient political structure at any given time--and, in that regard, Elizabeth II has served the country well by remaining beyond political commentary or involvement. As Queen, she embodies the history and tradition and culture of her subjects and she provides continuity which links both the past and present, something which is rather unique, and something that no elected official can provide. There is no other head of state who carries such cultural and historical symbolic weight, or who defines a national identity, in the same way, or with the same impact and respect, as the Queen. And there is no other head of state who can provide and transmit that same sense of enduring strength to her own people.
Even if the modern monarachy is largely a relic of the past, it may be a relic worth preserving, even in scaled down, somewhat less privileged, and more accessible form. The Queen, of necessity, has adapted to changes in that regard, and I think that, by the time Prince William ascends the throne, the monarchy will be considerably less remote and cloistered than it is now, and more functional beyond the mainly symbolic and ceremonial role they now play.
I recently read an interesting series of articles in Vanity Fair about Prince Andrew--his various tabloid scandals, his involvements with unsavory types (including his palling around with a convicted sex offender), his constant need to seek money, from sometimes questionable sources, often to pay his ex-wife's debts, etc.--all of which make him somewhat of a liability for the image of the monarchy, particularly in his position as trade ambassador.
According to that article, Prince Charles has intentions of streamlining the monarchy--starting with booting Prince Andrew's daughters from the royal payroll.
“My understanding is that Prince Charles was less than happy that Andrew was given the role of trade envoy back in 2001 after he left the navy,” Robert Jobson, author of William & Kate: The Love Story and a royal commentator for NBC News, told me. “When Charles ascends the throne—which he will do despite all the talk to the contrary—he’d like the royal family to be streamlined; he wants a smaller, more cost-effective monarchy. Andrew has made a tremendous effort to keep Beatrice and Eugenie close to the Queen in order to assure their future as fully paid-up members of the Firm, as the royal family is called. In addition to their status as royal highnesses, Andrew has always wanted them to have around-the-clock security and the rank of working royals. But if Charles has his way, the girls will be thrown off the royal payroll and have to fend for themselves.
A scaled-down, tax paying, clearly productive and revenue-producing monarachy would continue to be an asset, and that does seem to be the direction that it's been taking and will continue to take. And the clear appeal, and attractiveness, of the Duke and Dutchess of Cambridge is a real shot in the arm in terms of assuring a future for this monarachy and its ability to continue to evolve and adapt.