A slightly different direction: I’ve made tag rendering on topics and in topic lists show hierarchy breadcrumb-style: "parent > child’ instead of “child, parent”.
My solution was somewhat site-specific and rather hacky, but the end result is pleasing.
The biggest obstacle to what I did, and what you want to do, is that discourse doesn’t preload the tag groups so they’re not available when you need them without making an API request. I think it should, in the same way that the category structure is preloaded.