First of all a definition of what we mean when we say stripe SQL Server database backups. When we talk about striping a backup, it simply means the overall backup is distributed across several files, often on different drives. Microsoft’s description.
The biggest reason for me is the time savings. I’ve done a few performance analyses and in my various circumstances, the optimal number of files to create (for minimizing full backup time) has consistently been greater than 1, even when I’m writing all of the files to the same underlying drive. The only downside I see is having to manage more files.