I've wondered the same thing, guessing it's related to higher manufacturing costs for the rounded corners.
I think it's a manufacturing thing too. I just watched the "How it's Made" video on YouTube. When it comes to the part of separating each individual blade, the square edge makes snapping each blade off the roll look easy. If the ends were rounded, I think you'd have a waste piece between each blade. The older blades do look interesting though...
That was my guess. Less waste in the raw metal with squared edges and less waste on the blade itself (can't use rounded edges even if they look nice).
Gents today's blades are far better than the early blades. King Gillette envisioned a blade as thin as what is currently used but had to settle on the thicker blade due to the manufacturing techniques of the early 1900s. Nickerson (chief Engineer / Designer) did a brilliant job of developing those first blades, but the zenith of DE blades was in the 1960s/1970s (Stainless) when competition was fierce before cartridges took the scene. King Gillette was looking for the super thin blade (what we have today) to fit tight into the original curved OC he designed and in fact the OLD type OC design works far better with thinner stainless (or even modern carbon steel) blades. As to the rounded edge blade, in the early 1900s the cost and availability of Swedish steel was the reason why the edges were round to allow for structural integrity at the center of the blade while minimizing the amount of steel used while maintain a uniform size for honing and blade placement in the handle.
See folks, that's what happens when you have a book stuffed full of early Gillette newsletters. You've been warned!