The Bersa is a good example - is it a 1911? Being .45 doesn't automatically make the design "1911" in looks, just function.
1911's have that look because of the long flat sides on the slide, the proportion between the slide and grip, the locations at the rear, the controls, the rounded trigger guard. That Bersa might handle and shoot like a 1911, take the same ammo, but it doesn't look at all like one.
Same for the SIG P938 - it's a bit closer, but again, the cuts on the slide diminish the look. The grip is out of proportion to the slide, too. Overall, you can see it's derived from the 1911, but it has more of a older Colt auto look, primarily from the trigger.
Since caliber doesn't have anything to do with it looking like a 1911, the real issue is whether the downscaled version has the same proportioning left after all the monkey work is done.
It's the same for other guns, too, their are a lot of chopped versions of the HiPower out, it's just hard to see it. The slide stops right at the end of the barrel shroud, the butt is chopped to the point any curve in it is eliminated. There are some significant appearance clues left on the workbench next to the virtual hacksaw when that happens. It makes what is left that much more important in achieving the 1911 look. Mess with the spacing and looks of the controls, it's diminished even more.
No different than putting a '66 Mustang body kit on a Miata. Park one beside the other and it gets easy to see the differences. Chop half the hood off, shorten the trunk, and things become even more evident. Certain key items must remain unchanged to keep the connection to looking like a 1911.
As for "cool," that is highly subjective. One man's cool is another's fad junk. It's all in the perspective and how informed it might be.