cordorcet methods are overly complicated and don't optimize the right thing. the goal is maximal social utility in the face of strategic behavior. cardinal methods are simpler and generally better at this.
Apparently "candidate that would beat all others head to head should win" isn't the right thing? You'll need to explain that.
> maximal social utility
Some folks define social utility as erring toward more passionate voters, which is a potential problem with all cardinal methods. If they don't elect the Condorcet Winner, they are fatally flawed for any election that purports to be democratic.
https://electionscience.github.io/vse-sim/VSEbasic/