We have a similar system for electing the Mayor of Richmond, Virginia. It's biggest drawback is that the 2nd election is needlessly expensive, and since it's out-of-cycle and there are no other elections occurring at the same time turnout is much lower. I would prefer instant runoff.
I don't know about the costs, but here in Brazil the turnout for the second round isn't much lower: for instance, for the 2018 federal elections, the turnout was 79.67% in the first round, and 78.70% in the second round (source: official results website). But that's probably because voting is mandatory (except for voters younger than 18 years or older than 70 years).
