Difference of opinion for Steel-Dwass or Games-Howell post hoc test

[#1]

For a current study, group sizes for pairwise comparison are problematic, the group sizes are 15, 10, and 5. Because of the unequal group sizes and small sizes (additionally) the researchers are conducting a Welch's ANOVA. Following the Welch's ANOVA the researchers are conducting Games-Howell post hoc either planned or exploratory. The counter argument is being made that if the assumption for homogeneity is not met, the Steel-Dwass post hoc test is more appropriate. My contention is simply that the Steel-Dwass is a weaker test to follow a Welch's ANOVA, being a nonparametric post hoc test. The Games-Howell post hoc seems stronger. Help me see what I am missing. JMP 18.2.1

[#2]

A non-parametric test is stronger if the assumptions of the parametric test don't hold. You are correct that the parametric test is stronger if the assumptions hold.

[#3]

To muddy the waters, assume assumption 3 (homogeneity of variances) does not hold. Would the Steel-Dwass be the proper post hoc for a Welch's ANOVA or the Games-Howell still yet? If assumption 2, fairly normally distributed data does not hold, then one would use the Kruskal-Wallis and the Steel-Dwass?