Why aren’t any JP-1-type (extreme-narrow-cut) fuels in use today?
JP-1 is not in use because it's expensive and there's cheaper ways to deal with flash point and freezing point. 


The navy developed JP-5 for carrier use where a higher flash point is required, and it is easier and cheaper to produce than jp-1
A higher flash point isn't that big a gain in most use cases, it's not as if the fuel is going to instantly burst into flame if it reaches 40&deg;C - with good equipment and safety practices Jet-A(1) is still pretty safe to handle
Anti-gelling additives, tank heaters and recirculators work very well to keep fuel from gelling or freezing. This has proven very effective, BA-38 is the only case I can think of in recent memory where ice in fuel has caused an issue, and that was due to water ice crystals rather than the fuel itself, which didn't freeze. JP-1 wouldn't have helped in that case