Sometimes a game will need to be patched, or a MS update will indeed bork something, but going into diagnostic mode often vents your frustrations long enough to cool down sufficiently and accept that there's nothing you can do but wait for a fix. That said, sometimes it just takes patience. Once you do you'll go into diagnostic mode when something like this happens, instead of having a disc breaking meltdown. You just need to learn ways to deal with these kind of problems, as they WILL happen now and then on PC. PCGamingWiki lists fixes for both these crash types. For this it's recommended to increase the texture cache size. To fix that you have to copy and save the save folder, then delete the newest save.
On Bioshock 2, sometimes save files can get corrupted, causing a crash on startup.
It's a good argument for going Steam vs retail disc though, not that discs are commonly even an option anymore. Bet you wish now you'd come here before breaking those discs.