Tapes might be cheaper than HDDs but the tape drives are obscenely expensive to the point where it only makes sense to buy one if it would replace at least 100 hard drives.
With LTOs you have to kind of migrate every third generation onto new standard as well. Any given generation drive can read two previous ones, and write to previous and current. It's not a forever drive. Also, it's not also as reliable to story only one copy. It adds up, but still better than spinning rust.
Actually reading tapes from two generations back can decrease the lifetime of your drive considerably. So in a larger setup you're probably not going to want to skip as many generations (in part because you can and practically must incrementally upgrade).
What if we used the 1Gbps lines we have to our houses to sync data to a neighborhood level tape back system. We could just swing by the minimart and pickup some beer and our weekly backup on a datacart.
I think you are overestimating people's interest in managing their own data.
It isn't overestimation as much as willfull disregard for reality, if I outline my version of the universe eventually it will become true.
I like it. We don’t get anywhere without this sort of optimism.