Don't backup - replicate. Unraid instead of raid (Score 1)

"by erasing a RAID array on their home server" - don't use a RAID array. If it fails or you make a mistake, you lose everything. unraid is ideal for this. It isn't fast but it has disk level parity and a thriving support community to help. If you lose a disk, you can rebuild the array, and if you lose 2 or more disks, you only lose 1 or more disks of data - the rest of the disks are readable so most fo your data will survive.

'how would you backup 20TB of data?' - wrong question. Think instead how to replicate it off-site. My own setup has 16TB of films/music etc, and I have two 16TB copies at different sites which are loaded from a 1TB portable drive I move around. The bonus is whoever has the other servers gets to share your collection too.

Cost? - seriously, get over it. 3TB drives are mainstream and getting cheaper. HP's microservers are around £100 each and will take 5 drives.