Feels nicer to handle. No sharp edges. It doesn't affect reading at all.

I have a spool of blank blu-ray-r discs somewhere that are similarly rounded off, and caused me confusion about how proprietary nintendo's discs actually are.

Exactly, and it's not just about reading but also (perhaps even more so) about writing. If Nintendo control the manufacture of their proprietary disk, well, it's unlikely that a pirate outfit will be able to build a disk manufacturing factory that produces something compatible with retail Wii U's they can then sell their own non-Nintendo licensed games on. Or burn Nintendo's own games onto. The cartridge era of games were much easier to reproduce the physical medium onto, and this was super-widespread.

This did break down for Sony later on in a way it hasn't for the Nintendo Switch, a widely shared opinion on why the PS Vita flopped was because it was incompatible with standard SD cards _and_ that their own flash game cart and memory card offerings were so incredibly expensive. (And there were cheap SD-to-PSVita adapters that were released anyway. [0])

[0] - https://en.wikipedia.org/wiki/PlayStation_Vita#Hardware