Perhaps "true" self-referentiality was not needed. But it seems "dynamic feedback" is essential, and it seems to be adjacent to self-referentiality.

If we look at optimization process, it first does a forward pass which produces the output. Then it looks into computations which happened during the forward pass (by that I mean backpropagation), and adjusts parameters in such a way that it might produce a better output.

Formulated this way, it sounds like self-referentiality (system looks into what it just did!), but, of course, implementation is quite simple: it just stores activations from the forward pass. And training process includes not just code which does the forward pass, but also a full description of that computation which allows it to do a backward pass. So it's a kind of an unrolled self-referentiality which is not difficult to implement.

Perhaps more efficient learning can be implemented if researchers figure out a trick to avoid two separate, distinct passes. Our brains don't do a global backprop and are more sample-efficient.