To be a figurehead. They are seperate from the government for a reason (these days) and that keeps them independent. They do little for general society on the day-to-day, except for the tourism industry - others care a lot more about them than the Brits or Commonwealth do, but they do (or are meant to) be a moral compass for the population too. That's how figureheads have always worked.

Hence why people get very upset when they act like normal people - e.g. the Diana/Camilla/Charles years of the Early 90s. Or even worse, Andrew. Presidents are political figurehead positions, which means they make decisions that affect the day-to-day running of the country. This can be good and bad. Good because things come from the top, but also bad because if that doesn't work, the top is where the blame lies and there's no way to remove the top person easily - in a constitutional monarchy, the prime minister/head of government, can be easily removed by a vote of no confidence. Whilst the Republic system works well if the President doesn't have too much power, as was originally the case in the US for example and how it was set up, it becomes tyrannical if the President chooses to consolidate the power in the executive and, more importantly, is allowed to by the house - that's what the English Civil War was all about (i.e. the King wanted all the power themselves and the Parliament said no). Notice the parallels to the current US.