They can't learn iterative algorithms if they cannot execute loops. And blurting out an output which we then feed back in does not count as a loop. That's a separate invocation with fresh inputs, as far as the system is concerned.

They can attempt to mimic the results for small instances of the problem, where there are a lot of worked examples in the dataset, but they will never ever be able to generalize and actually give the correct output for arbitrary sized instances of the problem. Not with current architectures. Some algorithms simply can't be expressed as a fixed-size matrix multiplication.