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Thus, the things people are doing during interviews are the best tests we currently know.

This is, unfortunately, disastrously false. For example, we know -- via copious academic studies -- that work-sample tests are the best available method of predicting performance. Many companies in the software industry do not administer work-sample tests during job interviews. Instead, they have a disinterested person who you won't work with make up a random question on the spot (seriously, this is not only a thing that exists in the world, it is the default hiring method in our industry). The disinterested engineer interviewing you then spends most of their time preening about their own intelligence while ignoring your answer, and returns a decision known to be primarily determined by demeanor, rapport, demographic similarity, and other things which all decisionmakers will profess that they are not assessing for.

Do not pattern your internal decisionmaking off of software interviews. Software interviews suck.

[Edit to add: Incidentally, one of the reasons that one would predict "Well, clearly identifying talented candidates is important, so there is an incentive to get it right, so weak form Efficient Market Hypothesis suggests that companies are not freaking terrible at it." and still be disastrously wrong about the world we live in is that interviews have a principal/agent problem. The principal -- the firm -- cares a lot about extracting meaningful signal in interviews. The agent -- the engineer who is responsible for interviewing you -- is in no way rewarded for interviewing well. In many cases, their presence in the interview is already a strike against them because it takes time from doing the engineering work that they are actually scored on. They have not even the attenuated incentive to select good coworkers, because 90% of interviews result in No-Hire and of the remaining 10% the 95%++ case is that the new hire ends up working in some other part of the organization that the interviewing engineer will never need to meaningfully interact with. Faced with these very attenuated incentives for being a good interviewer, the engineer may instead to pay attention to more direct incentives like "get an ego boost by demonstrating my intellectual superiority over a captive, terrified, unable-to-resist audience."]

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