Why bother? If you make a CD drive to go into a computer (and not a stereo cabinet), why bother to have a lossy error correction method, when you must have a lossless one sitting right beside it?
C2 is error detection, not correction. C1 is the error correction. I think what wikipedia is trying to say is that the C2 error detection just points out something is wrong, even after the C1 error correction, and so you can't fix it. But a data CD has additional error correction, so it can correct more errors.
> but not on data CDs
Except when intentional errors are used for copy protection.