There’s been cases where people could take a conversation to private message, but instead the thread is simply bumped endlessly by exactly 2 people going back and forth. I’ve also had instances where I would’ve liked to just make friends with some of the people here, without having to post btags on the thread.
Edit: obviously you could disable the feature if you want.
The amount of toxic DMs that would go out might not be worth it though.
“might not be”
talk about an understatement 
Although I understand your examples, what you ask literally goes against the entire nature of General Discussion Public Forums. As toxic as it goes, creating private messages would be the final coffin in what little is left of community and interaction with strangers in this game. Everyone already is minding their own business with no social structures left in-game.
EDIT: Also, yeah… Blizzard would need to hire all those people they fired just to handle the Mod and reports lol
You could always just turn it off if you don’t want to receive any PM. Or make it so you click accept before reading.
There’s plenty of non-intrusive solutions to toxic PMs.
It’s a small enough request that I certainly wouldn’t object to it.
As long as I had the setting to make sure that no one can send me pm’s.
Why not just send them ingame mail instead?
I agree with Kazecap, the probability of abuse it too high for it to really be a good idea.
In reality if you are enjoying a conversation you could always share btag id amd transfer the conversation there. It’s a bit more clumsy but ensure acceptance from both parties.
So much of this. And with how little moderation there is to the forums, yeah, not worth it.
There’s simple ways to ensure acceptance from both parties without having to run through hoops. Heck, they could turn that entire process you described into a couple clicks, without diminishing the consent associated to it.
Or you could turn it off and go on like it never existed.
Nah I’m good.
But I’d be able to collect pro flight tears if it ever happened, I’m sure.
Sending very angry and hateful mails would lead to a disciplinary action in game rather than the forums . 
when I’m in a bombastic mood… a private message option i do not think would be good. Some people get really mad easily.
Then we can ERP on here too, I love it.
Ah yes, the ability to send anonymous hate mail is the one thing these forums desperately need.
I would love having DMs 
Or you can just email me if you want to DM me.
On the second one - you could do what I’ve done which is make a level one on their server and send them a letter. I made friends with Meritha that way after realizing that I enjoy their conversations.