I think this was one of the ones I looked at: https://www.trafficsafetymarketing.gov/safety-topics/child-s...

It notes this, which might be pertinent to your comment regarding how the overall statistics don't show the trends you expect:

> A NHTSA study found that while most parents and caregivers believe they know how to correctly install their car seats, about half (46%) have installed their child’s car seat incorrectly.

Here's a more quotable one that directly addresses your claim that it's compared with unrestrained: https://www.cdc.gov/child-passenger-safety/prevention/index....

> Car seat use reduces the risk for injury in a crash by 71–82% for children, when *compared with seat belt use alone*.

Here's another one specifically concerning booster seats: https://www.childrenshospitals.org/news/childrens-hospitals-...

> Children in booster seats in the back seat are 45% less likely to be injured in a crash than children *using a seat belt alone*.

That's about as much effort as I'm willing to put into this conversation. I'll finish off by saying I'm not American and these rules exist outside the US as well - I have a hard time believing so many countries would separately implement this (or similar) mandate if it was as unfounded as you claim.