Why can't my family member access the shared Apple Music family plan in their app?

The details:

• We have the Apple Music family plan, which is under my profile/email address
• The family plan is shared out to my family members, they can all see it under their family profile and what subscriptions they have access to
• Their home sharing setting in Apple Music is set to my email address, the primary account holder
• In their Apple Music app, I see their profile but there is no Apple Music account associated with their account (in the app).

I've tried everything suggested on this page but none of those approaches worked.

When I tried signing my wife's phone out of "Media and Purchases" — I tried resigning in as her, nothing. I tried signing in as me, and when I open up the Music app, I see MY profile and not hers... NOT at all ideal. I don't want her musical choices muddying up the waters of my preferences.

So Apple, what is the quintessential solution here? This is seems like such a fundamentally basic thing that should just work. But it doesn't. My wife and other family members should be fully signed into their profiles, and the sheer fact that their email address is listed in my family members, they should just automatically have access to Apple Music then. But nothing that I've seen here works.

I've logged her phone out, re-logged back in, tried turning it off and on again (thanks IT Crowd), my email address is set for Home Sharing. I'm at my wit's end here. I'd rather not have to purchase Spotify, thank you very much.

[Re-Titled by Moderator]