Is there any evolutionary reason why male traits appear in the heterogametic sex and female traits in the homogametic sex?
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.  (&quot;Male&quot; 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 &quot;ZW&quot; sex-determination system, which is essentially the inverse of the more familiar &quot;XY&quot; system.[a]  Other species don't have a heterogametic sex, but rather use lack of one chromosome as the determiner (&quot;XO&quot;, &quot;ZO&quot;), and yet others use lack of one half of all chromosomes as the determiner (&quot;haplodiploidy&quot;). 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] &quot;ZW sex-determination system&quot;, Wikipedia. 
[b] &quot;Sex-determination system&quot;, Wikipedia.