> The purpose of a head of state is to act as a personification of the state, so what better symbol could you pick?

There's no universal answer to that question. It depends on what you think the state represents.

In your case you attach a lot of importance to your state's longevity, in which case your rationale for the monarchy is consistent. But the defining feature of republican states (US, Ireland, France, most of South America) is definitely not their longevity. It is the idea that the state is a creation of the people, and that all power - real, ceremonial, even trivial - derives from the power of the people. In this case a monarchy is the wrong symbol, and the correct symbol is an elected head of state. (The head of state doesn't need to have power, e.g. Ireland's president.)