Several concept cars were involved, and I'll deal with four instances. The first is the 1954 General Motors Motorama show car Buick Wildcat II (link here). The next two were shown at the 1955 edition of Motorama (an elaborate traveling show featuring General Motors' production and concept cars). They were the Oldsmobile Eighty-Eight Delta (I have no decent link for it) and the Pontiac Strato-Star (link here). In those days, most of the best-known GM concept cars were what were called "blue sky" projects -- styling for its own sake and for corporate publicity purposes, rather than the thinly-disguised near-future production show cars that are so common nowadays -- though such cars might have a few features being considered for future production.
The final example is the 1956 Pininfarina Superflow I, built on a used Alfa Romeo 6C 3500 chassis. This link states that four different Superflow bodies were created on that same chassis as some kind of experiment by the coachbuilding firm. Only the first of the set had an unusual wheelwell treatment.
The Wildcat looks like it was a modified Chevrolet Corvette sports car. I base this conjecture on the shape of the windshield and cockpit area as well as the general dimensions of the car. The front fenders and the freestanding headlamps are a throwback to cars of the early 1930s and before. The two-level treatment of the front bumper recalls the 1934 LaSalle bumper. Spotlights on either side of the windshield were also found on some 1930 vintage cars.
All this is fine for a show car; the retro features become a fine topic for conversation. But those nice, polished wheelwell interiors would soon become covered in road grime from daily driving, so open fenders were probably never seriously considered as a future production possibility.
Apparently the concept of large front wheelwell openings became a fad at GM's styling center because something similar was used the following year. The main difference is that the 1955 versions were closed at the front, thereby eliminating the retro look on the Wildcat. Note that the rear wheelwells are also somewhat larger than usual.
The Strato-Star's front wheelwells closely resemble those on the Eighty-Eight Delta. Both sets of wheelwells are nicely finished and would be prone to becoming covered with road grime. What car owner would enjoy trying to clean off the mud, tar, and other materials that might gather there?
Another year, another impractical wheelwell treatment. I have no proof, but I wouldn't be surprised to learn that Pinin Farina and his team became wheelwell-conscious thanks to those GM show cars. In the case of the Superflow I, the front wheelwells are not elongated; instead, they have no tops. Well, there are tops, but they are in the form of translucent plastic fastened over the basic car body, taking the place of what normally would be an enclosed metal fender. Note the bullet-shaped headlamp housings -- something from the 1930s á la the Wildcat II.
Yet again, road grime and chips from gravel would doom this concept for practical production cars.