No, there is no particular reason that election results need to be presented quickly. There are legal deadlines that prevent election results from being excessively delayed — for instance, electors have a bit over a month to cast their votes in a presidential election — but that is hardly 'quick' by modern standards. In the 19th century, the general populace might not have known the results of a national election until December, because of or January; slow communication methods presented any faster dissemination. This is part of the reason that the new president isn't sworn in until January, to give (originally March); this gave the population time to learn of the results and prepare for the inauguration.
Modern US citizens tend to have shorter attention spans and to demand immediate gratification — functions of our mass-media-driven world — and Trump is currently working on those anxieties to produce fear and confusion (a typical part of his political strategy). But in the end, the election process will carry on at its own, slow, inexorably bureaucratic pace, and we'll be forced to wait and see.