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No, it’s a mitzvah like taking an esrog, which one must put in effort to do. Bitachon doesn’t exempt one from putting in the proper effort to do a mitzvah. I spend time and money looking for a nice esrog, I don’t rely on Hashem finding my basherte esrog.
I don’t necessarily think that there’s a strong indication that she can’t have children, but the issue is a legitimate one.
Your reaction is indeed overblown. Nobody is reducing this person’s value to her relatives’ fertility. Her prospects as a wife, not her value as a person, is being evaluated.