Okay, so. Bearing in mind that I'm pretty drunk? The short answer - about all I'm capable of at the moment - is that it became clear early on that it was easier and more practical to simply create either a fully-tracked vehicle, or to enlarge the wheels on a vehicle that you'd usually expect to see moderately rough terrain like a truck or weapons carrier.
In reality, the half-track came about as something of a stopgap solution to a problem that didn't really exist in the first place; developments in tyres and vulcanization would mean that you could get better and bigger tyres that were capable of inflating and deflating to a degree that meant they were able to traverse muddier terrain without having to worry about the complex track arrangements you'd see on a half-track.
Really, it's far easier to have a driver trained to change a tyre than it is to worry about whether or not your crew of fucknuts can whip off a track and change a suspension assembly under fire. Half-tracks came and went super quickly in the span of modern warfare simply owing to the fact that there were a dozen ways to do what a half-track offered even better, more simply, and with a fraction of the materials.
or as it was known in the field
THE MEAT CHOPPER
yes that's four .50 cal Browning machine guns in an electrically powered traversing mount designed for anti-aircraft operations-
oh
it fires at ground targets too??
oh that's how it got that name??????