Learn ASL because ASL is the language of deaf culture, CI can fail or need to turn off, CI may not work enough for all kids, a kid with CI still is deaf and ASL is the natural language, and ASL is a beautiful language to know for anyone. ASL is easier to learn as a kid. If later they need or want ASL, now why refuse to teach it? The parents can learn more ASL as the kid grows so they are good with ASL when the kid can communicate more.
The kid will struggle her whole life with communication - even with CI - so why would the parents refuse the work to learn ASL for a few years? Maybe the parent's work shows the parents a tiny bit of the struggle of the kid and new thinking about deaf and deaf community - another big benefit. It is hard to be the one deaf kid in a hearing family IME so the family knowing ASL is the hearing family trying deaf life for once - probably all other times everything is about the deaf kid being in the hearing world. So learning ASL is a small work for hearing parents to reach the deaf kid.
Just one example -
From Child: Care, Health and Development, volume 28 Issue 5 Page 403-418, September 2002:
A psychosocial follow-up study of deaf preschool children using cochlear implants
The aim of the study was to explore patterns of communication between 22 children with cochlear implants (CI) and their parents, teachers and peers in natural interactions over a 2-year period. The children, between 2 and 5 years old when implanted, had used the implant between 1 and 3.5 years at the end of the study. Analyses of videorecorded interactions showed that meaningful oral communication was more easily obtained in the home setting than in the preschool setting. Patterns of communication between parent–child, content and complexity of dialogues, quality of peer interactions, communicative styles of adults, and the use of sign language in communication turned out to be important factors when explaining the result of the CI on the individual child's development. The children with the best oral skills were also good signers.