Horrific Visions weren't roguelite. There was nothing really random about them apart from affixes.
This is heavily procedural with tons of randomization and replayability, not only due to the layout and encounters changing, but also your power progression options.
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As for replayability, there is a delicate balance they need to find. It can't just be something you play infinitely, because they want you to engage with the rest of the game. They don't want you to live in Torghast. So the logical solution is to make you earn runs through playing other content.
Though that's not necessarily the best option, I think. My gut instinct is rather than earning currency or keys to access it, maybe just have a limited number of runs per day (say 2 or 3) but let them stack over the week so you can save them up, maybe with a way to earn additional runs.
A sort of "soul fatigue" thing could also be done. Playing in Torghast fatigues you, playing in the world refills it, gaining anima (completing quests) fills it faster. Something like that. They could even use the exp bar to track it and have rest areas replenish it faster.