Interesting!

I personally don't think of blaming either gender, but I would blame patriarchal thinking, which is not blaming men or women. Patriarchal culture both heavily influences men and women in terms of how they think of themselves and their roles in society. Patriarchy is a way of thinking about genders and their roles in society, it does not mean men, but what society expects of men and women. Both women and men participate in patriarchal sexist culture and further it. Yes, women are often sexist too.

In patriarchal culture, a woman's physical appearance is the value she has in society. Most women I know who prefer tall men, explain it's because they want someone to make them feel small and little compared to their partner. When they are taller, larger, and take up more space, they are seen as less feminine and more masculine, so they crave men who make them feel more feminine and pretty, and pretty=little. Patriarchal culture plays a big role in women wanting to feel small and dainty which is considered beautiful as a woman because then you take up less space and don't bother anyone.

True, men are more prone biologically to be a few inches taller than women, that is genetic and biological.. However, what is considered desirable in a partner is very much heavily influenced by culture, not so much biology (though biology is a factor I must say). For example, for most of history, fat women were considered the most beautiful, the more fat the better, and actually the majority of men in many cultures at one point preferred fat women. And there are several countries in Africa where skinny is considered gross. There are even fat camps where tween girls go to be intentionally fattened up to become marriage material.

I'm sure there are also cultures in history where men being considered short is also preferred.

I think these ideas that tall men are better is a direct response of patriarchal culture, not necessarily biology.