Will, I think that the pluperfect "had fallen asleep" demonstrates separation from present state. Kind of disjunctive, or even concessive.
Present perfect can infer past action with an effect on the current state.
Pluperfect or past perfect means, as I understand anyway, totally completed, done.
Present perfect: "she has fallen asleep and therefore, she now snores."
Pluperfect: "she had fallen asleep, yet she continues to sob."
If the tense is deliberate, I think this could be the reason.

The simile refers to things that children presently are in the habit of doing, independent of the tense of the main verbal clauses.
Simpler one: "She hugged her son, as mothers do." It would be weird to say "as mothers did." We would have to ask why mothers no longer give hugs.
Also, the different tenses in the clause could be rendered ". . .as a child, having cried itself to sleep, (then) continues to sob. . ."

I often hear it used parenthetically, as if it means "as it turns out", or "as it happens to be", which is is not present contrafactual subjunctive.
Example: "He came, five hours too late, as it were."