“Rational”, what you’re saying is not at all rational, it’s apikorsus. Someone with that attitude cannot possibly help this woman, because it’s an example of the exact same problem she already suffers from. Going to a tzadik and asking him to daven for you is what Yiddishkeit says to do, it’s what our ancestors have done since the beginning of our people.
Kolev went to Chevron to ask the Avos for help. Yirmiyahu went there as well, and also to Moshe Rabbenu, to inform them of the churban and demand that they raise a ruckus in Heaven. The Jews on their way to Bovel stopped to invoke Rochel’s tears. This is the Jewish way, and we believe that it is an effective way to get a yeshuah from Hashem.
Nobody can know in advance whether it will work in any specific instance. The gemara in Rosh Hashana says that every Jew knows that when a Jew gives tzedokoh in order for Hashem to help him, and he doesn’t get the help he asked for, it’s not because Hashem couldn’t help him, or didn’t hear him, it’s because Hashem in His wisdom decided otherwise, and therefore he will not be deterred from doing the same thing again the next time he needs help.