I see the benefits of a graphological analysis as part of the shidduch vetting process because it tells you the character of the person at the time. Palm reading does not tell you that, it only predicts the future. Phrenology and physiognomy tell you only the traits a person is born with, also irrelevant. (Recall the story with Moshe Rabbeinu and the foreign king.)
From the research I’ve done, there seems to be plenty of theoretical basis for belief. I haven’t conducted any studies myself, but I have always gotten accurate results in accordance with the established beliefs when I applied them.
I don’t know if graphology can ever be described as a science. We can surmise that a specific stroke means dishonesty, for example, because 95% of crooks have that stroke. The same goes for cruelty. But is there a way to prove it? A personality trait can never be proven. We are not dealing with physical science that follow the laws of nature, we are dealing with the intricacies of human nature.
I am defending the validity of graphology here, not actively promoting its use in shidduchim. (And though I wouldn’t ask for a handwriting sample from a potential marriage prospect, I would be glad if I had the opportunity to see one.)
I believe an individual’s handwriting is a perfect reflection of his essence, with each pen stroke representing another facet. The only legitimate question would be if we are interpreting these strokes correctly. And that is a discussion for another time.