Why does WordPress want a 512×512 pixel site icon

The site icon in WordPress is worked as a favicon.

And the knowledge about the favicon is mostly limited to 16×16 or 64×64 pixels. But this StackOverflow thread shows there’s a necessity of a 114×114px favicon for Retina Opera, and a 200×200px favicon for Mobile Opera Speed Dial.

The necessity of such a larger icon is mostly to support retina displays, where it requires larger output, and smaller favicon can get pixelated. This article by Thomas Fuchs has a mention of 512×512px retina-ready favicon.

And I found this article with its comments stating that:

512×512px icon in the web manifest to support browser loading splash screens

Also found mention of other sizes like 192×192px, 228×228px etc.

So, with a maximum 512×512px Site icon, WordPress has all the ease to display it in different devices in different display ratios.

Finally this WordPress guide on using Site icon in WordPress could assist you.