I think it useful to separate our Monarch’s current, official role and purpose from what monarchies in general symbolise to people:
a) Our Monarch’s current, official role = domestically and internationally, ceremonially represent and promote the nation.
b) What having a monarchy in general represents to people = traditionalism, conservatism, colonialism, etc.
With that distinction in mind, what I say is that it is not obvious to me that the current, official role that our Monarch holds would be carried out any better by an elected politician. On the contrary! Judging by the sort of politicians we have to choose from; I’d much rather have the royals as ambassadors and ceremonial representatives of our nation than I would a politician in form of a president.
Humbly,
Hermit