Never thought about it from that perspective, but I think you're right. It is by design, not deceptive intent, just the infinite monkeys theorem where we've replaced randomness with pattern matching trained on massive datasets.
I do agree with the parent post. Calling them hallucinations is not an accurate way of describing what is happening and using such terms to personify these machines is a mistake.
This isn't to say the outputs aren't useful, we see that they can be very useful...when used well.
... but (a) we do, and (b) there's all kinds of dimensions of factuality not encoded in the training data that can only be unreliably inferred (in the sense that there is no reason to believe the algorithm has encoded a way to synthesize true output from the input at all).