I don’t think this strategy works well for individuals. Though maybe we are thinking of different reference sets. To me the way to understand social interactions is to look at what politicians do. Or if one only cares about a more intelligent set of humans executives at companies. People may hate politicians/executives but they are provably good at succeeding socially.
Are politicians/executives big on admitting weakness? I don’t think so. They seem much more fond of either blatantly lying (and betting their supporters will defend them) or making only the weakest possible admissions of weakness/guilt (“mistakes were made”).
Of course acting like a politician is usually pretty terrible for all sorts of reasons. But its probably the “playing to win” action socially.
It is suicidal to admit an actual serious weakness. For multiple reasons. One is that admitting a serious weakness will leave a very bad impressions that is hard to overcome. See the research that people will frequently pay more for a single intact set of objects then two sets of the same objects where one set is damaged.
The other problem is that admitting an actual error is going off the social script. It either paints you as clueless or a “weirdo.” This is also a very serious problem.