I did the roulette last night and got Castrum Meridanum. I queued as a tank, initially got an instant queue but someone pulled out; ended up waiting about five minutes.
I think we had five new players in the group* - at any rate, after the longer 'talking' cutscenes, the same five people were still in it for a few seconds more, so I suspect that first-time players don't get the auto-scroll on text boxes. However, if so, they seem to have timed the autoplay version reasonably well to people's reading speed.
* for what it's worth, Typhon has been a 'preferred' world lately so we may have a particularly high number of new people making their way through the story at the moment.
The final cutscene after defeating Livia can be skipped.
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Interestingly the cutscenes also now auto-play if you rewatch them at the inn. (I'd gone into it trying to get a particular shot of my character that looked good in the scene, but I was too slow to press the screenshot button.)
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Aside of more drastic changes to the gameplay, I think it would make sense to change the party setup to one tank and five DPS, like the alliance raids. (Reading through a guide now, the off-tank's job in Castrum is supposed to be picking up adds, but they seem to die very quickly now, and there's no real role for them in the Praetorium.)
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On getting the story experience vs. just watching cutscenes later - not only does watching the cutscenes 'in place' give you a better understanding of the flow of the story, but there is dialogue and events within the battles (eg. Hydaelyn speaking to you throughout the Ultima fight), and also it's not just about the content within the dungeon itself.
Once a new player exits the dungeon, they can't just go to the inn and catch up on what happened - they're straight into further story cutscenes and the end credits, then more cutscenes, then an in-game (thus unrepeatable) scene as you return to the Waking Sands and everyone greets and congratulates you.
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Also I just finished Heavensward main quest yesterday. It might be more efficient to have an empty dungeon without cutscenes, and then make you queue again for the final boss as a separate trial, but it feels a lot less epic from a story point (and I'm mostly here for the story). The Aetherochemical Facility, other than its boss fight, feels like a non-event. What was it for? Why were we in there? Just a jumble of passages and monsters for the sake of it.