I mean, there are definitely huge shortcomings in the "let's have the computer build the model from examples" approaches, and some of them are talked in the video, others are not :
- rare events are hard to train (that's talked about). The problem is that it's a long tail of unusual events.
- models generated can't be statically analyzed. You can't predict what's going to work and what's not. You can only hope. One very striking recent example is in this video : https://youtu.be/w2BWmSBog_0?t=220 . Here you can see that an AI trained on the model of AlphaZero managed to reach 3223 elo rating (so, far beyond human), yet it blundered its queen. And that's just chess, where every rules are written in advance.
- Models don't build human knowledge. That's more of a philosophical point, but imagine a perfect AI built on neural networks after having read all human knowledge. What can it teaches us ? AlphaZero chess isn't able to provide any clue or explanation on why it favors one move instead of another. You can only learn buy playing against it, but that's all. Not even the developpers can tell you what advances in chess theory has AlphaZero made.