In a religious court, one has to judge, and excessive compassion interferes with justice.
The Talmud describes an act of compassion done specifically by women.
Maybe this is another reason they cannot serve as judges in a religious court?
Maybe they are more suited to serve as judges in a house of compassion?
Does that make sense?

I think I’ll delete this whole thread.
You’re quoting a Talmudic text and asking me whether it makes sense. Is there something there that bothers you? Then write what it is. Beyond that, you started with testimony and ended with judgeship. You write the explanation as if it were obvious and then ask—I don’t know what. I expect someone who asks a question to invest a minute in writing it before expecting me to invest time in writing an answer (and of course also in deciphering the question).

The Talmud says what happened.
I’m asking whether that could be a reason (even if it’s not written explicitly) to disqualify women from serving as judges (and maybe also from testimony), because they are compassionate.

Yes, in principle it could, in the sense of the rationale of the verse—and there is more to say about the fact that we generally do not derive law from the rationale of the verse. Though one should remember that the elderly too were disqualified because of excessive cruelty. Moreover, this reasoning is mainly relevant to capital cases, lashes, and punishments—criminal law—but in monetary law, for example, compassion does not necessarily tilt the scales; compassion toward one party is cruelty toward the other. Third, this speaks about judgeship, not testimony. And since the Talmud links disqualification from testimony to disqualification from judgeship—with the exception of one Tosafot view regarding Deborah the prophetess—this explanation is not likely.