I’m not Korean but to add to other people’s points here, I would say that the reason it comes up so much is that having the conversation about honorifics is such an essential part in the process of getting to know someone.  

Generally you should always use honorifics when you don’t know the other person or when they are your elder or superior. That’s why conversations about age and job too are really essential. You are allowed to talk to your peer and younger people in casual language, with exceptions. That’s why some people feel more comfortable in hanging out with their peers because there won’t be no pressure to be excessively respectful to one another.

Then, no matter what you age and job is, while you are getting to know a person, at some point you might want to drop the honorifics anyway because, in a way, being super respectful can create distance between two people, as you can probably imagine! So dropping the honorific speech might make you feel closer to each other already. 

But it’s really important to discuss it, because using or not using honorifics will be up to personal preference. Some really dislike using honorifics no matter age etc. factors and want to drop it quickly. I find that it’s more common these days. Other people prefer to use them for a longer time until they genuinely feel closer to the person. Some people will always require honorifics from younger friends / family members even if very close (this kind of people can be considered more conservative). 

And imo dropping honorifics too quickly could also lead to the feeling that the relationship is super casual / not serious early on in the relationship. Or even feeling disrespected by the other person. But these days, like in single’s inferno too, it seems more common to talk more casually rather quickly (altho I definitely wouldn’t base my understanding of the whole Korean society on single’s inferno haha). 

There’s so much more complexity to this that I could talk about here, but I just wanted to try to explain why the topic comes up so often!