Apparently the reason the installations were fucked up was that a portion of the game got corrupted on the store servers, and the Xbox One itself had no way of handling the corrupted files. So when you tried to uninstall, the corrupted portion stayed on the drive and it became impossible to remove /overwrite it. Given the uniqueness of the issue it took 343i, CA, the Xbox OS team, and the store team a while to figure out, but apparently the OS team has a fix now. I don't know if it's in the most recent OS update or not though. It's also the reason the most recent few patches have triggered full game downloads - the store team completely flushed the game from their servers and replaced everything, which caused everything to download again in the update process.
At least, that was the case of the issue that I was having from September or so until a earlier this month. I don't know anything about May.