The problem with cloud-based solutions is that the cost for backing up several terabytes of data is typically several orders of magnitude higher than building your own RAID array
Nonsense. One order of magnitude more, at most. On-line storage costs are on the order of $100 per TB per year. There's no way you can build and maintain your own solution for $1 per TB per year, which would be two orders of magnitude less. "Several" orders of magnitude would be at least four, putting you in the range of a $0.01 per TB per year. Even $10 per TB per year would be tough to reach, if you want any redundancy, and if you value your time at all -- and while you're amortizing the cost of your up-front hardware investment over several years in order to get close to that level, on-line storage costs will continue dropping, so at the end of those years the savings would be even smaller than they appear now.
Plus, backup storage which is located on-premises is inherently inferior to off-site storage, because a whole range of disasters that take out your primary storage whack your backup, too. Fireproof safes are a partial solution, but not a complete one... and not a cheap one.
No,the best approach is to use a cheap, unreliable, local backup, not bothering with bunkers or safes or even much redundancy, plus use an online service. The local copy is your normal recovery source, the online service is your final fallback.
Personally, I just replicate my data to a couple of local machines (the machines are there anyway, so throwing a little more storage in them doesn't cost much) and keep another copy on Google Drive, which is $120 per TB per year, but I managed to get 1 TB free (in perpetuity) as part of some promotion, and I currently have just under 2 TB of data that I care about (mostly photos), so my net cost is about $60 per TB per year for the online component, plus another $25 per year for an extra 4 TB drive that cost $100 and I expect to get four years out of (will probably go longer, but could die sooner).
Upload time sucks, but only for the initial upload, which I did two years ago. After that, incremental additions are pretty negligible. A full restore from the remote copy would take a long time, but I can easily get individual files on an as-needed basis. Actually, I find I use the remote copy quite frequently to grab particular photos or files on various devices, so it provides some functional value as well as disaster protection.