I think the trick to making them appear smooth is having edge pixels with varying alpha values. The images I produced had fully opaque edge pixels. As a test, I made a palette version of bknight.png in Ultimate Paint. When I loaded the palette version, the edge pixels no longer had varying alpha values. As a second test, I saved a 24 bit true color version, and it also had lost the varying alpha values on edge pixels. Finally, I saved a 32 bit true color version, and when I reloaded it, it retained the varying alpha values. I also tried the latest version of Paint.net. When I selected the option to save it with an 8-bit depth, it offered the option to set the Transparency threshold, and it said "Pixels with an alpha value lower than the threshold will be fully transparent." So, I'm thinking that having varying alpha values is available only in true color images, and that provides a reason for keeping these as true color images.
I think the trick to making them appear smooth is having edge pixels with varying alpha values. The images I produced had fully opaque edge pixels. As a test, I made a palette version of bknight.png in Ultimate Paint. When I loaded the palette version, the edge pixels no longer had varying alpha values. As a second test, I saved a 24 bit true color version, and it also had lost the varying alpha values on edge pixels. Finally, I saved a 32 bit true color version, and when I reloaded it, it retained the varying alpha values. I also tried the latest version of Paint.net. When I selected the option to save it with an 8-bit depth, it offered the option to set the Transparency threshold, and it said "Pixels with an alpha value lower than the threshold will be fully transparent." So, I'm thinking that having varying alpha values is available only in true color images, and that provides a reason for keeping these as true color images.