1) It happens ALL the time, just as many guys will not go out with a girl who is not a size 2 or 4.
2) It shouldn’t happen, but no one has a right to tell another person what they should find attractive or not.
3) My daughter is 5’2″ and went out with many guys who are short (under 5’6″ by most standards of average height). Even though she prefers taller guys, she wanted to give it a chance. She came to realize that she is actually physically uncomfortable looking right at a guy’s eyes at or close to the same height as herself. This is a personal preference, and no girl should be condemned for it, unless she is being really unreasonable and refusing to even consider an othewise perfect (on paper) shidduch for even one date. But if she likes to wear non-flats, and he is shorter than herself by several inches when she is WEARING flats, that makes many girls self-conscious.
4) My dad O”H was several inches shorter than my mom. Never bothered her, because he was a giant in Limud Torah, brilliant in his secular knowledge, and expert in his field, bringing relief from physical pain to many people, often at no charge when they could not afford to pay.
5) The bottom line is that girls AND boys have the right to feel attracted to their spouses. If lack of height is bothersome (and many guys also do not want shorter girls, because, “they show weight gain faster”), then that person cannot be convinced to feel otherwise. That is, unless they reach a point at which they recognize that shidduchim are dwindling, and they need to re-prioritize.