Genuine question here, so why don't all passengers sit rear facing? Why aren't cars designed with rear facing passenger seats?
I believe the answer to this is quite boring and unsatisfying - because it's always been that way. A lot of things are like that. There are cars with rear facing seats (usually people carriers with a reversible row) but because they aren't so sought after that people will preferentially buy them, and most adults prefer facing forwards (e.g. on a train) it's easier/cheaper for car manufacturers to just keep doing it like it's always been done.
How much safer actually is it in percentage terms?
It's hard to say exactly. A study a few years ago came up with a figure of 5x safer but it was later retracted because the maths wasn't right. I also feel like it was a bit misrepresentative to say 5x safer. The figures in that study showed that forward facing child seats reduced the chances of injury/death in an accident by 60% whereas the rear facing seat reduced them by 92%.
Which gives you 8% injury chance vs 40% injury chance (but bear in mind this is 8%/40% of the chance your child would be injured if they were completely unrestrained). The 8 vs 40 is where the "5x safer" idea comes from, I think. To me it is more like saying the FF seat is 5x more risky. 60 to 92 feels like about 1.5 times safer. And because this was children up to age 4 you can assume that this is concentrated at the younger ages.
In case studies where they look at accidents where children were killed or injured in forward facing seats the numbers seem to come out fairly consistently that about a quarter of the time it wouldn't have mattered what seat they were in, whereas about 3/4 of the time they would likely have been less injured or uninjured in a rear facing seat. But also if you look at some of the case studies they are things like one year olds in booster seats or they are very old data with old seat types we no longer use because the design of them is inherently dangerous (like the T-shield seats from America).
In crash tests where they can measure the relative forces on a crash test dummy, the loads are about 5-10 times higher in a forward facing seat compared with rear facing. That doesn't mean much really unless you look at the threshold for injury - but essentially FF seats tend to be over the threshold whereas RF seats tend to be under it.
I did at one point find figures which led me to an understanding that at least for children up to about age 2, bearing in mind that the injury rates of unrestrained children are MUCH higher than for adults, being rear facing reduces their injury rate roughly to the rate of adults who are wearing seatbelts, whereas being forward facing reduces their injury rate to the rate of adults who are not wearing a seatbelt. However, I can't recall how I came to these numbers so I don't want to quote it as some kind of authority. It is quite stark because we are so used to seatbelts for adults as being an absolute necessity.