Militarily, the NKPA didn't have the strength by the time
What if North Korea won the Korean War and took over the entire Korean peninsula? Is this possible? How would the Cold War be affected by North Korea having won the Korean War? What would this alternate Korea be like(likely it would be pretty bad)? Maybe a more isolationist US is needed, but is it possible that if Kim takes all of Korea the US and allies would find it too hard to win any back? How would history be altered? What if?
Militarily, the NKPA didn't have the strength by the time they reached 8th Army at the Pusan Perimeter; a straightleh infantry army with limited artillery and air support, very little armor, and no seapower at all, was not going to break through the lines that 8th Army could maintain - they came close in a couple of sectors, but 8th Army could and did trade space for time to bring firepower to bear.
The most likely way to get a DPRK that controls the entire peninsula is for the Soviets to get to Pusan before the US forces landed there in September, 1945 - which was three weeks after the Japanese surrender and a week after the ceremony aboard USS
Missouri; the Soviets had - barely - the seapower to get troops into southern Korea before the US could, and the agreement on where to divide the two occupation zones was not final 17 August 1945. The Americans were concerned about the Soviets occupying the entire peninsula, but the situation was very fluid, planning was minimal (the focus was on Japan and the overseas Japanese garrisons), and the Soviets might have been able to present a fait accompli.
That leaves a unified, Communist Korea, without the devastation of the 1950-53 war; paradoxically, given the relative speed of the Soviet movement into Korea, in a relative sense, not that much damage was done by the Soviet invasion.
It's possible the DPRK remains a fairly stalwart Soviet ally, doesn't go as (relatively) bad as it has historically (absent the impact of the 1950-53 war and the subsequent garrison state), and there is some sort of Glasnost-like movement when the USSR dissolves. Whoever the DPRK's leadership ends up in such a situation (it may not be the Kims et al, after all) they may become something of a "Tito's Yugoslavia" type power in northeast Asia, able to play the Soviets and Chinese off against each other ...
Possible, at least. One can hope.
Best,