More than anything else, its the grip
The .357 Mag is long. 1.290" case length. This compares with the 1.285" of the .44 Mag. A fraction under 33mm case length. Compare this to "service" class auto pistol rounds, and its huge.
Rounds close to the .357 Mag have been done for the auto pistol, the 9mm Win mag being one. The Automag IV was chambered in 9mm and .45 Win mag. The problem is the guns are big, have large to huge grips, and are not even remotely in the service pistol category.
Only a few people like magnum autos. The are too big for many uses. Too expensive, don't hold enough rounds for some folks, don't offer "advantages" over revolvers, etc.
I have all the first gen magnum autos made during the 70s-80s, and the smallest of them is the Coonan. And it is still significantly larger (and heavier) than a full size 1911A1.
Next would be the LAR Grizzly, which is bigger yet.
Magnum autos are specialty pieces. Like ALL autos, you can't run mild and wild loads without modification (the exception is the Wildey, with an adjustable gas system), like you can in all revolvers. This turns some folks off. You can't make double stack mags, and still get you hand around them (unless you are Andre the Giant), this "lack" of firepower turns some folks off (these same folks see revolvers as hopelessly short of firepower as well).
Magnum autos can't be all things to all people. In the real world, they haven't been enough things to enough people to claim a significant share of the retail market. Only the Wildey and the Desert Eagle are still in production, and Wildey is only made in very small numbers, compared to the DE.
You could build a double stack polymer frame rimless .357 magnum auto pistol, but damn few people would buy one, except for collectors
, and fewer of them would actually be able to shoot it! One advantage of the big heavy magnum autos is the weight damps the recoil, some. A polymer frame magnum would be a real bear to shoot, even with a (single stack) grip that you could hold on to!
As to the .357 Auto Mag (.357AMP), it is the .44AMP case necked down, and will shoot bullets of equal weight nearly 500fps faster than the .357magnum revolver round! Small numbers of the Grizzly were chambered for the .357 GrizzlyWinMag, a dimensionally identical round to the .357AMP, using the .45 Win Mag as its parent case.