Would a Mass Effect with computer-generated dialogue for NPCs work?

Intriguing idea but no. I like having real people voiced characters not some computer.

I think it could work as long as each NPC had a defined range of responses based on their roles in quests and the world in general - it wouldn't make a whole lot of sense for an archaeologist to give you dialogue explicitly related to being a physician or biologist, for instance - but it would take a colossal amount of labor to implement, and ultimately the people who would actually care about it are not in the majority of players. Plus it would have to generate voice acting too since having VAs record enough words and phrases to make this system believable would be unrealistic. While simulated inflection is definitely getting better (just look at Siri or Alexa, for example), it still doesn't really compare to a well-directed human voice actor.

I think this technology has the potential to become a trend in the industry in about five years time, but it's not ready for prime-time yet.

In time this will most certainly become a thing but we're not there yet to be using it fully.

I suspect that this kind of thing would play out like other forms of procedural generation - people will pick up the patterns and soon you will hit a "lack of depth" sort of roadblock.

This could be countered by explicitly adding several layers of "depth". But then you get into the little matter of "how do you design and implement the game?"

In other words, I expect this approach to make the easy things easier and the hard things harder.