king of america
The lack of a separate head of state. For you non-political-science majors, a "head of state" is the person who is top dog in a country; this is distinct from "head of government," the person in charge of the actual governing apparatus. The easiest way to explain this is by turning to Britain. Queen Elizabeth II is the "head of state." David Cameron, the British Prime Minister, is the "head of government." Head of state can handle ceremonial duties and represent the country; head of government gets much less pomp and circumstance, and focuses on policy and governing.
A head of state does not have to be a royal or hereditary position; in Germany for example, an elected president is head of state, and a chancellor (prime minister) is head of government. The best model for a head of state is one with extremely limited powers. The British monarch is a good example, as is the German president. They can take certain actions on their own in extremely limited circumstances; otherwise, they concentrate on representing Britain/Germany as nations, not on representing the Cameron or Merkel governments.
In the US of course, the president must handle both duties, the ceremonial and the political/governmental. As Kristoff observes, this eats into a president's time. It also has the unfortunate aspect of politicizing even ceremonial, supposed-to-feel-good things the president does with his head of state cap. For example, some complained that President Obama was not going to Arlington Cemetery on Memorial Day (never mind that Reagan never went, Bush the Elder never went, and Bush the Younger usually but didn't always go. AND never mind that instead Obama was going to attend similar ceremonies at ANOTHER military cemetery in Chicago, also the final resting place for American servicemen.) The criticism was mostly from the right wing, and it was mostly just another chance to dis Obama. But if it had been an American head of state doing this, the "let's score political points" angle would not have been a factor.
I'm not a fan of absolute monarchy or hereditary power. But a constitutional monarch or similar head of state would have great advantages. Ronald Reagan I thought was a pretty poor head of government - disconnected, possibly not quite all there at the end, and overall a poor set of policies. Reagan, however, was a wonderful head of STATE. He was classy, enjoyed the ceremonial duties, could project empathy (which nowadays would disqualify him from consideration for the Supreme Court according to some Republicans). Reagan was great in consoling family members and the nation at the memorial for those killed on the Challenger.
I don't expect we will ever had a separation between head of state and head of government. But it would be nice.