To some degree, you've answered the question. When there is a second round, the outcome necessarily represents 50% plus one of the voting population. Conversely, in a system based on the plurality of votes, it's possible for members representing 25% or 30% of the population to be elected. Someone could slip in between the two majority party candidates, for instance, which would be much more representative of the views expressed by the vote. Someone would still have a week-long period to more strongly and thoroughly assert their positions, since it's possible they would have to represent the majority of the population going forward. As I see it, that member's voice would be even more powerful because it would represent 50% plus one of the voting population.
On October 3rd, 2016. See this statement in context.