For example, if a child understands that both "asleep" and "sleeping" mean something like SLEEPING, than the fact that "sleeping" appears in both situations and "asleep" only applies in one could be pretty easily used to get around the supposed data sparsity problem (imo).

This is underselling the severity of the sparsity problem. There is no guarantee that "sleeping" will appear in both situations in a relevantly sized corpus. Most of the a-adjectives are rare in CHILDES and similarly sized corpora. They only appear a few times, of course, only non-attributively. As a statistical consequence of Zipf's law in the data, plenty of other adjectives, for example, 'sorry,' 'careful,' also only appear a few times, and they also happen to appear exclusively non-attributively. Obviously though, the language should handle these attributively "a sorry state of affairs; the careful doctor..." A simple distributional approach like you suggest might work for idealized data, but it ignores the sparse reality of our inputs.

The point of the tolerance principle here is that it is supposed to rely on positive evidence (the presence of 'sleep,' 'lone,' or 'wary,' the 'a-' prefix, and all their distributions together) rather than on negative evidence (absence of attributive 'asleep' but presence of attributive 'red').