From Diablo Wiki
A "bottomless dungeon" or "endless dungeon" is a common fan request for Diablo type games. The desire is for a play experience that never ends, or that grows steadily more challenging, as opposed to the usual Diablo-style play experience of repeating the same few areas of content in every game.
There has never been an endless dungeon in a Diablo game, and when asked about it the Diablo 3 developers answered with questions; what do players want when they say endless dungeon? What sort of gameplay would that allow or create, and how could it be done better or more quickly?
Ultimately the developers created Nephalem Rifts which function much like an Endless/Bottomless Dungeon, as they allow for endless randomized replayability within the same game.
The developers answered questions about Endless Dungeons many times after Diablo 3's release, always saying they liked the idea and were experimenting. In retrospect, the developer replies are clearly leading up to Nephalem Rifts, which were not revealed until late in 2013. Without naming Rifts in advance, the developers talked about more varied monsters, more varied layouts, allowing for long term play sessions in the same game, etc.
Travis Day, in April 2013.
At the heart of that idea is something really compelling, wave events, endless dungeons, hold out missions etc. Standing as the lone hero, or one of a party of heroes, against an onslaught of demons really sells the fantasy of Diablo, it’s just a matter of taking the seed of that idea and iterating on it to a point where it feels like it fits into the game as a piece and not just “the only thing to do”.I do hope that down the road we can find some way to make that idea a part of the content options players have at their disposal. I’ve said one numerous occasions, in a perfect world, when a player sits down at their computer for the evening to play the Diablo the question I want them to say to themselves is “What do I feel like doing tonight?” not “Ok time to run Act 3 again”.
Josh Mosquera and Wyatt Cheng interviewed by IncGamers.com in July 2013, a couple of months before Nephalem Rifts were announced. You can see from their answer that they're basically describing how Rifts will work, but obviously without naming them in advance of the reveal.
What happens is players start… like it drives you into starting gameplay styles. We saw this some at release, where maybe you make a super tanky defensive build, which is effective, but not very funto play. Yeah, I can beat something, but it took sixty minutes of kiting. Which is really fun and exciting the first time you do it, but isn’t something we really want to encourage people to do en masse.
But I think that the idea that there is greater challenge out there is cool. I think the idea of I want to test my character is cool. I think the idea of this game is too easy and I would like a great challenge is cool. So the desire behind those is cool, but the design of a dungeon, where every level is progressively more difficult, we found didn’t work.
3:50 — Josh Mosqueira: The core of what Wyatt was saying now is… all those things you mentioned in the question, they’re things we’re thinking about. To be specific without necessarily getting into the details, I absolutey think that the intentions of providing players with more ways to play the game… for me that’s a key pillar of taking Diablo to the next step. And the concept of an end game for everyone.For us to really articulate that, we’ve been thinking and prototyping as many different vehicles of gameplay that will allow all our players to find something interesting to do and to constantly shift their objectives as they play the game.
November 2013, from a Blizzcon panel after Nephalem Rifts had been revealed as their answer to Endless Dungeons.