5% of non-sleep time is 48 minutes a day. Do you think that's a good estimate of the amount of time children spend around their parents? It also seems likely that parents would have a disproportionately large impact compared to their share of the time- among other things, their personalities will be mostly constant whereas a rapidly changing set of peers or teachers would have a wide range of personalities.

(About 50% is heredity, and so if we assume all of the rest is effects by other people, we could go up to 10%- 96 minutes- but I think the best explanation is low variation among parenting styles masking the impact that parenting style has on children. That doesn't have to mean there's much room for benefit above a mediocre style, that there's room for detriment below mediocre would be enough).