JP-1 was the first U.S. military standard jet fuel (hence the 1 in the designation), with its specifications issued in 1944; it was an extremely narrow-cut, high-alkane kerosene, not far from what would later become RP-1. As a result, it had both a very low freezing point (-60C maximum) and a very high flash point, a combination that is the Holy Grail of the aviation-fuel industry. Its only drawback was that it was hard to produce (since, to quote John D. Clark in Ignition!, “not many refineries in the country could produce such a product with their available equipment and crudes”), and therefore expensive and in chronically short supply, which prompted the development of wide-cut fuels (first the extremely-wide-cut JP-3, followed by the somewhat saner JP-4) and the gradual disappearance of JP-1 (although, judging by mentions in various aircraft accident reports, it apparently was still being produced into the 1970s).
On the other hand, those were 1940s/50s refineries that had difficulty producing JP-1 - and what would be tough beans for a 1940s refinery would be no trouble at all for a 21st-century refinery, thanx to the polymerisation/cracking/hydrogenation/witchcraft/etc. techniques originally developed to turn all the heavier, less-profitable petroleum fractions (and the gaseous, hard-to-store ones) into gold, I mean gasoline, which could easily be adapted to turn even the most recalcitrant crudes into extreme-narrow-cut, JP-1-type fuels (especially given that RP-1 is an even tighter kerosene than JP-1, albeit not by much, and yet we haven’t had any trouble getting ahold of that in the vast quantities needed for launching things into space); so why haven’t we returned to JP-1 and similar fuels, which have freezing points rivalling Jet B combined with flash points that blow away (pun intended) even Jet A?