GODzilla
Have you tried what this guy is claiming on EA HQ ?
Load the game and once you are in the game disconnect your internet connection:-)
Sounds like a weird thing to do
But as I said before I have to disable my second monitor in order to play the game :-)
I tried putting both Origin and offline mod and not logging in ingame. I played for around 10 hours this way and my experience is a bit ambivalent.
I believe that during that time I heard less music and banter did not increase. When I switched back to online, music got more obvious, played more often, at least thats what I heard.
Now this could very well have been pure coincidence / bad luck, I don't know. I have to admit that I tried this for no reason really, because banter was playing at a satisfactory rate even without any trick - but one: Traveling via war table.
I did this from the very beginning and while it triggers another bug - battle music upon return to Skyhold, stops when you visit the war table and then exit it so no big deal - this seems to have kept my banter working right from the start.
Patch 1 and Patch 2 did not change anything, I'm sure. As of Patch 3 I will have to see. A quick test yesterday, just arrived in a new location and I heard some area- and quest-specific banter ("free men of the dales" stuff) right away.
PS: *switching to easy greeting mode* ...
*knocks on the table* welcome everyone. 
PPS: I never owned a console but am not against consoles. If you see me using the term "pc masterrace" it's purely for fun and I'd never really engage in a flame war for one or another gaming platform. I even own an XBox360 and XBoxOne pad for pc and played some games with it, which benefit from gamepad, like Castlevania LoS or Remember Me. 