@sunnystrict1 We have a Republic. In a Democracy each person gets to vote on the leader. Under our system each state votes for the leader (ostensibly each state is individually a democracy that then defers to the republic of the states) but electors are not constitutionally held to vote in accordance with the popular vote of their state. The electors may be fined by their state if that states laws require them to vote based on the popular vote, but those are state laws not constitutional or national ones.
Further reading on constitutional electors and the electoral college can be found in article 2 and in amendment 12
The political system that works best is dependent upon the country it belongs to. Saudi Arabia and the Gulf monarchies would, in my opinion, be better off as secular republics, but the monarchies of Denmark, Norway and the Commonwealth Realms do not necessarily (at this moment in time) require a deposition in favour of a republican form of government.
If a monarchy becomes problematic (e.G. The monarch works against the country or its interests) then it should definitely be abolished; if Charles, Prince of Wales, was a terrible King, and so was the Duke of Cambridge, then it might be right to consider a British republic.