I'm not sure what you mean by "the most important physical trait in a male". Women prefer taller men. They say so and studies back this up. Taller men have more mating options and more attractive partners. Taller men make more money, and they are more likely to be selected as leaders. They are perceived as more dominant and more attractive. It is utterly indisputable that in western societies at least, being above average in height is a huge benefit societally for men.

Do taller men have more children? Apparently not, but that's kind of a horrible metric for success in a modern society, because people are actively choosing not to have as many children. More interesting questions might be how height affects frequency of sexual encounters, or number of sexual partners, or any of a number of other measures that most men might want to increase, vs number of children, which is a number that most men do not want to increase significantly beyond the average.

Actually, an interesting question might be too ask how many children a man wanted compared to how many he had. Do taller men end up with more, less, or the same control over their reproduction?