For personal backups (unless you're the king of personal Big Data) tape doesn't make sense in most cases.
Where tape shines is for offsite copies, DR copies, or duplication for safe keeping of any kind, not backups.
Tape will work for backups, but you have to structure your working processes around tape (serial access) to the backed up data. If for you "backups" includes rapid access to an old version of a file you edited or deleted by mistake and pulling in data that's too old for you to want to keep on expensive disks so you can process it, tapes aren't a good option, for reasons of access time.
Most modern IT professionals would use NAS or SAN snapshotting to handle the first case above, where you did an oops and need a copy of the file as it was before that. A snapshot directory on a NAS usually gets implemented using a journaling file system or some other mechanism for maintaining a point in time view of the system, so you're not keeping another complete copy of your data, only journal entries listing what changed when.
For the second case where you have too much data to fit on your expensive SSDs and you might need to use some of it e.g. next week or next month, what you want isn't tape, it's a cheaper hard drive. IT types usually call this "near line storage". State of the art spinning hard drives are a good option, but if those are still too expensive you can go a couple generations of technology back and get lower price/TB. The problem you run in to doing this is that you need more physical space and hardware and power/cooling for the lower capacity drives.
Tape is great for when you want to keep data but may not need to access it ever or might need to access it months from now, and when you can accept a delay in access of a day or two. DR copies, offsite vaulting of data for legal purposes, logs from systems you want to keep in case you ever need to check back on what happened 5 years ago, bulk data from experiments that may never be accessed again but which could be critical for someone if it's needed (and may therefore turn out to be extremely valuable)... those are the scenarios for tape, and the price per TB stored is lower than anything else.
The company where I work off sites data for long term storage regularly, including a copy of our main ERP database. We meet legal compliance requirements the cheap way by copying stuff to a tape we can access and paying someone to store it for us. Backups of production systems are done to disk, to a NAS or SAN block storage device that is then copied to tape if needed.
Edit: Forgot to mention the ERP databases' size... it's in the Petabyte range, it runs the entire company. If we tried to transmit it to a cloud backup provider, without spending a giant amount of money on a high speed internet connection we'd never complete a daily backup before it was time for the next one. On top of that, if we need 2 copies of it the storage price gets very high very fast - cloud storage is very convenient, but costs more than even local spinning disk. Tapes,on the other hand have a small incremental cost if we already have the drives and robot, and we can make as many copies as we like by paying only for the tapes and the time.