[chalst]

My understanding is that very short men are handicapped by not wanting to face the stigma associated with being shorter than their partner, and that tall women face a comparable difficulty finding partners.

The issue here is not so much that men do not find women taller than themselves attractive, but the second-order concern about drawing attention to their own height.

I have the impression that it is typical that men usually become less distressed by such stigma when they get older.

[gridlockd]

A far simpler explanation is that females want the best for their offspring, being fairly tall is generally an advantage in every aspect of life and it's hereditary.

Generally, the preferences and concerns of disadvantaged males do not matter. Females choose the males, and they almost universally choose taller males.

[chalst]

Your explanation ignores the difficulty tall women face finding partners in wealthy countries and so addresses only part of the data. E.g.,

"In western postindustrial cultures, taller women tend to have less reproductive success (RS) defined as number of children surviving to reproductive age, than women 0.7–1.7 standard deviations below average height"

https://doi.org/10.1016/j.evolhumbehav.2008.06.003

[gridlockd]

Fair enough, here's the missing part:

Tall women have trouble finding partners because women not just want a tall man, they almost universally want a man who is taller than them. It's the same for high-earning women, they almost universally want a man that earns more than them. The same is true for education or job status and many other factors, and they compound.

https://en.wikipedia.org/wiki/Hypergamy

Women who are exceptional in one or more of these traits face a commensurately smaller pool of men that are acceptable to her, whereas every man in that pool is attractive to a commensurately larger pool of other women. However, men are not hypergamous, they do not care about earnings or education and they prefer shorter mates. Therefore, the males in that pool are more likely to end up with another female than the exceptional one.

Unable to find an acceptable partner and absent societal pressure in western societies, those exceptional females may defer or give up on reproduction.