Having runoff elections allows for another round of campaigning and the voters can make a more informed choice given the results of the first round. There is some value in that, but personally I'd lean towards instant runoff or just proportional representation etc.
That value of continued campaigns should be weighed against the requirement that voters need to vote multiple times. Depending on how the votes are cast (in-person vs. mail-in, precinct-based vs. county-based, etc.), subsequent rounds of voting would likely see diminishing voter turnout.