I never really understood (unless I try to disconnect reality and travel back in time to the days when SQL was created and tape drives were directly attached to the database servers) why this option exists. Using a single file for multiple backups is completely outdated. Really, even backing up to individual files on disk is somewhat outdated given the power of current backup software. Using a hierarchical model in our backup software, we keep multiple days worth of backups (either fulls & logs or just fulls) on disk. Those are migrated to tape for offsite and longer term retention during the day.

If all you have available is standard SQL backups and the integrated tools, then certainly individual files, in a scheme that meets your business requirements will keep you out of your bosses office. A strong redundancy/backup solution above and beyond the free tools, or better still, a replication strategy to an off site location, may keep you from needing the backup for more than something to fill your spare time.