In short: it was cumbersome and expensive, and became less necessary over time.

The inventor of the fifth wheel, Brooks Walker, actually kept innovating on the system until he died in the 70's, and he tried several times to bring it to market. In 1952, when he tried to sell it to Cadillac as an addon, it was reported that it would cost $175, equivalent to around $1700 today. More pressingly, though, the complicated mechanical system took up all of the trunk space in the car.

The next year, he was able to mount the system on the continental kit of Chevrolet Cavalier without sacrificing trunk space (like this), but Chevrolet turned him down. I can't find much reliable information on why he was turned down by Chevrolet, so I won't speculate. Again, it could be any combination of cost, maintenance issues, or perhaps even licensing demands by Walker who owned the patent, but I don't know.

He continued his efforts, mounting the system on a 1957 Oldsmobile Stationwagon, an early 1950s Ford stationwagon, an early 1970s Saab Sedan, and others. All of these required significant modifications to the car, including cutting open the bottom of the car, changing seat alignment, making the third seat face rearward, and extending the rear fender. In my opinion, none of these efforts lived up to his continental Chevrolet Cavalier which required minimal changes.

Ok, so Walker's efforts didn't pan out, but why didn't anyone else keep trying once his patent expired? Presumably, with enough work and funding, it could've made a feasible addon. We're in speculation territory here, but over time parallel parking has become far less common. The rapid post-war suburbanization of America meant that most of the middle and upper class people who would be driving cars with this luxury addon had spacious, personal garages and driveways. Instead of shopping on a Main Street with on-street parking, they started shopping in commercial malls and department stores with sprawling parking lots. Even commuting to work in the urban core, there were now metered parking garages and parking lots they could use instead. While they definitely still needed to parallel park, they usually didn't need to do it enough to justify the expense of the addon. Plus, in the last few years, high-end brands like Teslas or Chevrolet Malibus have added auto-parking features using sensors. As that technology becomes better and more common, there will probably never be a need for a fifth wheel.