
I don't see how you can wear out a disc from playing it too much. There's no moving parts to actually wear out and the lasers aren't powerful enough to cause damage. Writable discs maybe because that's slightly different, but not legit game discs that have been properly pressed and sold as a finished product.
The only real way to 'wear out' a disc is from not looking after it or faulty hardware.
I played the scuba minigames in New Leaf so much that my A key became unresponsive, but I've never broken a game before.
I don't think I've broken any games as the way you described, but there is a HUGE black spot on my blue Gameboy Advance SP since my brother and I have had it for about a decade. We have both put a lot of use into it and I don't plan to ever get rid of it.