The homogeneity tag seems to map to "heteroskedasticity"
This is problematic because homogeneity of variance is not the only form of homogeneity people are interested in.
Consider, for example, this post, which I have been trying to improve (still a work in progress, I'm afraid, I started with trying to give it some context). He seems to be trying to follow the advice in this paper, or perhaps to follow the analysis in Wijngaard et al (2003)*.
The OP was asking about homogeneity, so wanted to use the 'homogeneity' tag (n.b., the tag doesn't specify '... of variance' so that's perfectly reasonable). But it just replaces that reasonable use with the misleading tag 'heteroskedasticity'.
Consider also the chi-square test of homogeneity of proportions. Someone might (again, legitimately in my opinion) want to use the homogeneity tag... with a rather unfortunate result (especially if they don't notice that it silently changes).
If the tag was 'homogeneity-of-variance' I think the argument for such a merge would be strong. But without the 'of-variance' I don't think they're necessary the same thing at all.
What should be done about it? I'm somewhat disinclined to simply say 'you can't use the homogeneity tag to talk about homogeneity'.
* J.B. Wijngaard, A. M. G. Kleink Tank, G. P. Konnen, (2003),
Homogeneity of 20th Century European Daily Temperature and Precipitation Series,
Int. J. Climatol, 23, 679-692.