Why don't modern PCs come with error correcting RAM? Bit errors in RAM happen, whether due to cosmic rays or hardware failures. Estimates vary: an error every 3 days on a typical PC or maybe every month. A survey of Google's servers came up with 8% of DIMMs seeing at least an error a year. Whatever the exact rate, odds are a typical modern computer is going to see some.
Do RAM errors matter? Sure! For example, at Black Hat Artem Dinaburg introduced bit squatting, where you register domain names one bit off of popular names and wait for random errors to send traffic your way. He reports getting close to 100 hits a day off of just 31 domain names. Sam Pullara reports he's able to duplicate the attack.
More generally, RAM errors cause random data corruption. They are entirely preventable with error correcting RAM. Indeed, the early PCs all had parity memory (error detection, not correction). ECC adds a little access time overhead and some expense for the extra RAM and ECC logic. But isn't it worth it?