One of my biggest frustrations with e-mail as long-form discussion like this is misunderstanding points. Someone will write paragraphs of text arguing their position, but they made a bad assumption or missed something simple at the start that either partly or completely invalidates the rest of what they are saying. Depending on if people realize this or not, it's easy to slip into a kind of bike-shedding discussion arguing about the incorrect details. I've been on both sides of this, and it's one of the reasons I dislike e-mail for it.
I tend towards being an introvert, and I'm not always good at coming up with an argument on the spot. I recognize this, and I will often end the real-time discussion by literally just saying "Ok, I need to go think about this before we discuss it anymore. Let's come back in a day or two." Just like you don't have to respond to e-mails the instant they come in, you don't have to do it for real-time or chat, either.
I will also do the same to others when I can. For example, yesterday I suggested a new approach to how a certain part of our product works, and pitched it to the team. There was only minor feedback so I just said "okay, go think about it, and I'll bring it up again later", so I will probably ask tomorrow to see if anyone has further thoughts on it. It's amazing what sleeping on ideas can do.
The thing I'm really trying to get at here is real-time doesn't mean "now! now! now!". There's absolutely nothing wrong with several meetings over the course of days or weeks or months. For strategic and key design discussions, there should absolutely be documentation written between those discussions. In fact, that's basically the way I operate: discuss, document, give time for people to review, and then discuss again, repeating as much as needed.
There's people that are opposite and want the response "now!", and don't want to take time to think through problems -- but I would guess there's a large overlap with the type of people that come over to your desk / call you and say "I just sent you an e-mail, did you get it?" and then only read the first sentence or two of your reply anyway.