The psychology and history of forward-facing seats has been answered well already here. I ask instead about how bad it is that seats are forward-facing.
For context, I was looking through Wikipedia's list of airline flights that required gliding, and a surprising fraction of the 30 incidents listed were fatal to some, but not all, of those aboard (47%). Averaged across the 30 incidents we get that 25.1% of those aboard died (noting that this average is pretty unscientific, and is subject to sampling and coverage biases; it's still interesting). Even among just incidents with fatalities on average less than half of those aboard died! I generated a scatter plot of the incidents:
This data surprised me a lot! My layman's intuition says that emergency landings should be a lot more bimodal, with basically all landings either being gorgeous US Airways 1549 style happy endings, or blazing fireballs with no survivors, with some very rare exceptions. Based on this intuition, I always figured it was reasonable that passenger seats face forwards; I thought "rear-facing seats wouldn't help that much anyway, edge-cases where it would have made the difference will be the rare exception to the rule".
But is this really true? It seems that maybe many deaths on commercial flights are incidents in this intermediate region, although I don't have the expertise to evaluate if rear-facing seats would help with how people typically die in commercial airline accidents.
Question: As a really rough ballpark, how much safer would commercial airline flights be (averaged across all commercial flights globally) if the seats were rear-facing?