Because the app icon is used to generate all of the sizes, having a higher fidelity icon means sharper icons when they are downsampled (if we wanted to be pedantic, 576 is the LCM of the Android variants and would be a better choice than 512 when it comes to scaling). Eventually, for iOS we will also need to provide a 1024x1024 image in the app bundle for the App Store, so it made sense to pin the size to the needs of the various app store platforms (it needs 18 different variants). Note that anyone can also include an icon that's larger than 512x512 (or smaller, as @Diego pointed out), but in the end they will all be sized to the expected values.
For reference, the default App Inventor icon we use in this release is actually 1024x1024, and it is 67 kB. All of the icon variants that get generated are 166 kB, so the icon payload for an app is around 230 kB. Figures will vary depending on how compressible the icon data are.