I’d enjoy it. In fact, I clearly do it: there is a difference in how I engage with a bestie that I banter with constantly (like, say, Zeibura S. Kathau) and a friend of a friend, one of whose answers I was impressed by.
But… I can make that distinction in my head, because I recognise my besties. I’m not clear what additional functionality or UI distinctions Quora needs to add. I think I’m more friendly to social networking use of Quora than Konstantinos Konstantinides is; but like him, I don’t see what value it would add for Quora to make such a distinction in its interface.
If you have something in mind, OP, I’d be interested to hear it; but be aware that Quora, as far as I can tell, has never been enthusiastic about the social networking use of Quora.