Why don't major social media introduce relationship management features?

That's a good question. I would say that, to some extend, they do with their core features. Facebook shows you updates from the people you are connected to. It also tells you when it's someone's birthday. It shows you memories.

Now, I haven't used Facebook in years and I have no idea if people rely on it at all to maintain relationships.

Several companies have tried to launch "personal crm" but none really managed to make it a thing (yet?).

My hack is to I have a project in Todoist, with recurring tasks to touch base with my friends, clients, family, etc. It also has birthdays.