Is there any evolutionary reason why male traits appear in the heterogametic sex and female traits in the homogametic sex?

Question

If you define male as the heterogametic sex, and female as the homogametic sex, then my question sounds like a tautology. But, what I'm trying to get at is why is it that the traits we associate with "males" (e.g. having an unlimited amount of possible offspring, greater average height, etc) appear in the heterogametic sex, and why traits that we associate with "females" (e.g. having a limited amount of possible offspring, shorter average height, etc) appear in the homogametic sex. Or, is it simply by chance that the homogametic sex became the female sex and the heterogametic sex the opposite?

As far as I understand it, heterogametic chromones allow for a greater chance of mutations being displayed, so I wonder whether there is something advantageous about this occurring in the male sex rather than the female sex. Perhaps it is because males are more "expendable" since they can have an unlimited number of offspring? Is this line of reasoning accurate, and are there any alternative explanations that go deeper than this?

Answer 1

The title question,

Is there any evolutionary reason why male traits appear in the heterogametic sex and female traits in the homogametic sex?,

suggests that male always is the heterogametic sex, but this is not true. ("Male" is usually defined as the sex with the small, mobile gametes, i.e. sperm, as contrasted with the large, nutritive gametes, i.e. ova.) There are many species where females are the heterogametic sex, such as birds, most snakes, some fish, crustaceans, and insects.[a] These species use the "ZW" sex-determination system, which is essentially the inverse of the more familiar "XY" system.[a] Other species don't have a heterogametic sex, but rather use lack of one chromosome as the determiner ("XO", "ZO"), and yet others use lack of one half of all chromosomes as the determiner ("haplodiploidy"). Others don't distinguish sexes by chromosomes, but use environmental stimuli.[b]

All this variety in forms of sex determination suggests that there are not substantial evolutionary advantages to having the heterogametic sex be the male.

[a] "ZW sex-determination system", Wikipedia.
[b] "Sex-determination system", Wikipedia.