Aren't YouTube captions good enough not to violate the Americans With Disabilities Act of 1990?
No, auto generated captions are gibberish. Try watching a complicated lecture on a scientific topic but turn down the volume and only look at the automatically generated captions. Not only is there a high error rate but there is no punctuation. 

Note: the DOJ findings letter is online  (mirror) and you can see the legal rationale behind  the findings of law.

It should be noted that other universities followed the law when they implemented their MOOC programs and captioned their videos from their videos from the start. UC Berkeley was warned by its own academic accommodations committee in 2012 that the way they were implementing their MOOC was not only a violation of their own policies but would probably result in a violation of the ADA, especially given their status as a public university.

Furthermore, contrary to media reports Berkeley was not "forced" to take down the videos. The complainants from the very beginning (circa 2014) wanted to engage in an interactive process that would ensure access, even if over time. Berkeley declined to engage which resulted in the complaint being escalated to the DOJ. However, even the DOJ letter did not request a takedown. This was entirely the decision of UC Berkeley's senior administration