They already do extensive road safety studies for speed limits, lights, signs, etc. I believe fatal accidents are required by law to be extensively investigated. The less serious ones usually receive some investigation (they want to cite someone). Most of the time accidents are caused by driver error, such as inattention, not knowing the law, or simply making bad decisions. The laws and road design are usually sufficient if the driver is doing their duties correctly and responsibly.
> The laws and road design are usually sufficient if the driver is doing their duties correctly and responsibly.
Here is where the problem lay! Expecting drivers to always be attentive, lest they kill someone(or multiple people) is not a sane way to reduce traffic fatalities and injuries. You stated it yourself that driver inattention / error is a contributing factor in most crashes. In NYC, driver inattention / distraction and 'Failure to yield right of way' are the two largest leading causes of pedestrian and cyclist injuries and fatalities[0].
Sure, better education can reduce the likelihood a crash happens, but it does not reduce the severity of a crash when it happens. Reducing the severity of crashes means designing infrastructure that keeps the most vulnerable road users safe.
> I believe fatal accidents are required by law to be extensively investigated
I can't speak for most places in the USA, but in NYC this is entirely false. There are many instances of NYPD showing up to fatal crashes, asking the driver(who just ran someone over) what happened, and then just taking their word for it. It usually takes a team of lawyers at the behest of the family of the deceased to actually gather evidence[1][2]. A councilmember in NYC recently proposed a bill to get NYPD out of crash investigations for this very reason[3]
Sounds like NYC is just lazy, similar to how Philly cops wont even show up to an accident unless someone is hurt. Many states have fatal crash units that are part of the state police, for example NJ. I would guess that NY does too, but that NYC uses NYPD instead of the troopers.
Reducing the accidents is the goal. There are safety studies done prior to installing new infrastructure or when deemed necessary due to accidents. There are already things like bike lanes, crosswalks, plastic bumpers, etc to keep people safe. Education and testing is the best solution as it would provide a reduction of fatalities not just in the cities, but also on the highways. You can see that the fatality rate is about double compared to countries that have stricter tests.