Autoassociation is definitely important, not only for disambiguating noisy patterns, but also to form better representations in general (see the success of generative and autoencoding models in traditional ML). And as you say, neuroscientists find it all over the place.
It is, but it's implicit in the formulation. As you mentioned there is temporal autoassociation, although that could be seen as different because the "rolling autocomplete" is happening at a high rate. But consider the more stable representations at the level of temporal pooling, as you go up the hierarchy.
Although it would be a massive oversimplification to consider the cerebral cortex to be a strict hierarchy, the hippocampus is widely considered to be at or near the top. As a result, you would expect very high level abstractions to form there, and that is exactly what we see (e.g. place cells).
So when you've got temporally pooled high level representations, the key is that they change slowly enough for autoassociations to form (the pattern persists for longer than a few STDP windows). While a temporally abstract representation is active, it can form connections with not only the input that triggers and sustains it, but also recurrent connections that can help it complete itself in the face of ambiguity as more information comes in.
These recurrent connections onto temporally abstract representations might form on distal basal segments, that would gel with the existing theory. Then the autoassociation would be in the form of "predictive" depolarization that encourages pattern completion. But the exact mechanisms are definitely still an open question.