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Recently on a Third Eye Drops podcast, I heard them say we will need to go through a dystopian period before emerging into a utopian one. That rang true to me.

I wonder how long a period like that could or would last

In that conversation, they were talking about anywhere from 100-300 years. Not exactly an exact science. ;)

The term used was "technodelic utopia".

I think you'll enjoy this conversation:
http://thirdeyedrops.com/mind-meld-58-microdosing-future-michael-garfield/

The part I'm referencing starts around the 48-minute mark, but the whole thing is worthwhile. Lots of great philosophical tangents with these two guys.