Whole-disk vs. per-file encryption address different threats, and aren't really comparable.
YES: Most filesystem-level backups (ZFS a possible exception, not sure) are vulnerable to the kind of data corruption or device failure you're talking about. If you don't have all the pieces you don't have a chance of decrypting. Filesystem resiliency (let's just call it availability) and infosec (confidentiality, and they can share integrity) don't always have common ground.
If you're seriously worried about a few bad blocks (or tracks, or sectors, or salt-water soaked boot tapes, whatever is appropriate) there are definitely ways to work around that, erasure codes and appropriately sized and distributed chunks of data come to mind (taohe-lafs, for example).
It seems that what you're really asking is should there be one big basket or a lot lot more little ones. It's difficult for anybody to answer that for you.
EDIT: The above answer is obviously incorrect. A single damaged sector will not result in complete loss of data. Recovery of files from an encrypted filesystem on physcially damaged media is unquestionably more complicated and less reliable than from an unencrypted one. Regardeless, backups should always be encrypted.