in particular the President, Lord help us, take on the role of the Monarchy and Monarch in the UK as a figurehead of the state, and a repository of national pride and identity. IMO, this creates a far too reverent view of the apparatus and potential of state, if not of the particular people who inhabit that apparatus.
Ironically, separating the two seems to make a more sophisticated view of the process easier as national pride and the (notional) role of politicians are more easily compartmentalized in the mind, assisting greater objectivity. Expectations of the government are lowered to something, IMO, more realistic. Politicians are temporarily employed managers, a matter of necessity, convenience and practicality, not the embodiment of some kind of fantastical ideal or the totemic mascot of a team. They don't even have to pretend to be.