I suppose you haven't watched it. Neither have I. It's great and lovely. Kate Middleton, a daughter of flight attendants, found something that many girls dream to find, namely her prince. And the courageous prince whom I consider an utterly positive character has found a pretty babe, too.
Some nations remain monarchies, some nations became republics after they abandoned all the artifacts of feudalism. We did so in 1918 when Czechoslovakia was created. After a millennium of the Czech Kingdom, which had been a part of dominantly German-speaking empires for most of the time, a key to independence from the German-speaking masters were allies in the U.S. and France, so it was pretty much guaranteed that we would reproduce much of their republican systems and abolish monarchy, too.
Does it make a difference? Which system is better?
First of all, it doesn't really matter much. The main difference resulting from a monarchy is the existence of one additional family of celebrities who are celebrities just because they belong to a particular family. Capitalism and democracy in the U.S. and the U.K. don't differ much. Neither do the legal systems.
Let me admit to the U.S. readers that throughout the 10 years I spent in America and despite my great and gradually increasing admiration for the U.S. founding fathers, I had no strong opinion about whether the independence - or the loss of a major British colony - was such a great event. The crazy king wanted you to pay taxes, didn't he? Well, the non-aristocratic leaders including Barack Obama often insist on the same thing. You had smaller capacities to influence the British politics? Well, that's because you lived in a province used as a storage for prisoners etc. It was different than today but it did work, too. And even today, with the U.S. democracy, it's still true that people's wealth does depend on the place of birth - even though the change of the functional dependence since 1776 may be viewed as being beneficial for the U.S. territory. ;-)
In the case of Czechoslovakia, to pick an example where I know details, the kingdom was formally abolished but the president has literally inherited much of the perceived status that used to belong to the king. So he (and maybe in the future, she) enjoys an immensely high approval rate and everyone finds it appropriate that he is using the Prague Castle, a highly representative place formerly associated with the kingdom, as a place to work and show his appearances.
The first Czechoslovak president Dr Thomas Garrigue Masaryk was a "daddie" of the Czechoslovak nation and he was almost universally loved. His successor, Dr Edvard Beneš, a bright man largely chosen as the successor by Dr Masaryk himself, was viewed as the political and intellectual elite of the nation - and he also became the mirror of the hopeless situation of the democratic nation when it faced Nazism as well as communism.
The approval rates of all the communist presidents were between 100 and 105 percent. It's not just the communist fabrication that was playing a role. I think that even largely anticommunist ordinary people would have some respect e.g. for Mr Gustáv Husák, the last (Slovak) communist president of Czechoslovakia. Mr Husák fought against the Nazis and was later, in the 1950s, given a life in prison by (other) communists. His predecessor Mr Ludvík Svoboda - the president who unfortunately became a tool to legitimize the "normalization" regime after the Soviet destruction of the 1968 Prague Spring - was a top general leading a group of Czechoslovak soldiers who came from the USSR and helped the Soviets to liberate our territory.
In all cases, including the era of late communism since the 1960s, the president has been chosen so that he (or she?) is awarded for some of the life-long achievements and courage. In this sense, he's analogous to a king. The approval rate of President Klaus fluctuates around 70 percent despite the fact that he used to be controversial as a prime minister, with the approval rate often slipping below 30 percent. He may still be controversial in some circles but he has become a representative of a large majority of the nation, anyway.
This figure of 70 percent is impressive given the obsession of the Czechs to complain about everything. It is much closer to the 80 percent approval of Queen Elizabeth than to 47 percent approval rate of Barack Obama or the 20 percent approval rate of Nicolas Sarkozy, the current leaders of republics that inspired the republican character of Czechoslovakia in 1918. Our president, much like the Queen, is a person who is allowed to be so much above everyone else that he doesn't really participate in the confrontations that people consider to be divisive. He is paid enough so that the people don't have to think about the ways how he steals things. (And when it is about a pen, everyone knows that it is just some fun.)
Now, of course, there is a striking difference. The status of a king or queen is hereditary. This has consequences. While the first feudals had to be exceptional people, or they have at least done some exceptional things which earned them their titles, nothing can guarantee that the same description applies to their arbitrarily distant descendants. But does it?
I don't know. I think that the royal families across the world are OK but in some sense, they're no longer "genetically" exceptional. (Let me avoid comments about their inbreeding that doesn't seem to be too frequent and far-reaching today, anyway.) Most of their special skills may be reduced to social effects, especially to the wealth given to them by the people of their kingdoms. With a lot of money and with some traditions, it's not shocking that you may become much better with the horses and in golf. The young members of royal families may also be trained to speak many languages, and so on.
But are they better, for example, in science? I think that it used to be the case. While the background of top scientists used to be diverse, and parents of great scientists could have been both superpoor as well as hyperwealthy, I think that the wealthy people were overrepresented - and not only because of their families' better access to education.
I am not sure it is still the case. In particular, I am not aware of any member of an aristocratic family who is extremely good in theoretical or particle physics. (Of course, most of the explanation is that the Jewish nation doesn't have too many aristocratic families.) Even if I have forgotten about someone, or if I am unaware of someone, I think it is fair to say that these folks are not surely overrepresented in the top physics community. ;-)
Instead, the royal families are largely what the tabloid press makes out of them: celebrities analogous to actors and singers who are being watched on every step. They're trained in skills that can be appreciated by the most average citizens. When a prince tries to act as an intellectual who struggles for far-reaching and long-term results, his being an average thinker usually badly manifests itself - and William's father is one of the most obvious forbidding examples. If a few more people targeted by the tabloid press and the hereditary character of the ruler are the only major differences between a kingdom and a republic, I don't think we're losing much by not having a monarchy anymore.
The other differences are infinitesimal and I don't think that they're terribly harmful for the monarchies, either. Of course, I am talking about some constitutional monarchies only. An aristocratic dictatorship makes it way too easy for the ruler to prevent progress for long decades which is a bad disadvantage in the modern world. Democracy is hugely imperfect but its ability to self-regulate still makes it a better system than the previous ones.
However, when some special people - who differ by their financial security throughout their life - just influence the society in some way, I don't think it's bad at all. Hunger is a good cook but a bad adviser, a Czech proverb says. Because ordinary people's chances of becoming a king or queen - and Kate Middleton and her colleagues are the only exceptions - are essentially zero, the jealousy aspect evaporates, too. Monarchies can work but they're not necessary.
