Quick thought experiment, what if republics - in particular the idea we elect our rulers - had evolved straight from monarchies, rather than, as in reality, often as a result of a violent rejection of said monarchy.
I propose we'd see the following titles
Presidents would be called Kings (or Queens) but would be elected, just as the President of the United States is elected.
Governors of States would be Dukes
Leaders of Counties would be, of course, Counts
And Mayors would be Barons
There are also intermediate ranks, as many places include another level of government between county and municipality, and the title of Viscount would fit in here.
Between King and Duke is Archduke. Between Duke and Count is Marquis.
I'd presume that all elected officials would be Esquire, and that such a title would be regulated so that you could not simply claim to be one.