> Can you? How would that work in practice? Isn't this just "he said/she said" with no way to resolve it

Conflicting claims or testimony are common in the legal system, and we do in fact have means of resolving them. They are not, of course, 100% guaranteed to resolve things correctly, but it is simply false to say that there is no way to resolve it.

You didn't really answer my question, you just assured me that your opinion is right. What could be used here, exactly? Like, suppose I accuse someone. They say they didn't do it. There's no physical evidence or witnesses at this point, so there's no way to deduce anything from impartial evidence. What can be done here to decide who's right with any worthwhile degree of confidence?

> You didn't really answer my question, you just assured me that your opinion is right.

Its not an opinion; whether we have a method of resolution is a verifiable question of fact, and the answer is yes, we do.

Juries make decisions where the key evidence is conflicting testimony of two witnesses all the time, where the other evidence, if any, isn't directly on the primary question but the reliability of the witnesses.

Usually, this will resolve against the accuser where the US criminal standard of proof (beyond a reasonable doubt) applies, and have more mixed results where lower standards, like the preponderance of the evidence or clear and convincing evidence standards used for various purposes (e.g., usual judgements and permanent restraining orders, respectively) in the US civil justice system, apply.

Whether this resolution mechanism has satisfactory results is, of course, a subjective question.