To expand on the first problem...

You can always rerun a backup job if the tape fails, but one of the most common times for a disk drive to fail is when it's stressed, and this is frequently during backups.  So your disk drive will fail while writing to your only backup tape - no disk, no tape.  Kiss your data goodbye.

Have I seen this in the past?  Yes, I have, multiple times, and all of those locations have since been re-architected.

Tape drives don't belong in remote sites unless you've got real data centers and real operations staff.

Our business folks do not want to mount/unmount tapes for weekly and incremental backup.

Then you need tape libraries, not tape drives.  And that still assumes you have real data centers to put them in.  Don't even think about putting a tape drive or library in an office environment unless you like dealing with failures caused by heat fluctuations, dust, and all of the other stuff that people tolerate but equipment doesn't.

   .../Ed