How exactly are you ensuring that there exists a candidate who has been ranked on at least 60% of ballots? The only way I can think of is to require voters to rank all of the candidates (or a bit more modestly, at least 60% of the candidates), but this opens the door to a lot of strategic issues. For instance, suppose candidates A and B are each the favorites ~50% of voters and the second choices of ~50%, and virtually nobody likes C or D. Here, if a few people dishonestly vote A>C>D>B (instead of the honest A>B>C>D) they'll give the election to A as this will give A more support than B in the decisive second round. If enough of the electorate votes dishonestly like this you'd have C or D win as the "consensus" choice.

Even guaranteeing a majority is impossible (see https://voting-in-the-abstract.medium.com/the-problems-with-rcvs-majority-claim-e7b748f5079c). Promising a supermajority goes even worse.