As someone who used to admin a 30PB+ LTO library I love me some tape, but unfortunately it’s not that simple of a value proposition.
Bit rot is less of a thing with LTO, but still a thing.. I.e. you will at some point need to update your LTO system and it’s storage media.
The robot I owned was the library storage for movie frames at a major motion picture studio. We would upgrade every other release, so while I was there we were upgrading from LTO-5 to LTO—7.
The robot was big, and would write data to two redundant tapes. One copy would be sent to Iron Mountain, the other stayed in the robot.
Creating a backup like you are isn’t really protecting much if you don’t have a good facility to store the tapes in.
Part of the point of paying for a service like AWS Deep Glacier is that it’s an offsite backup.
An LTO backup has no advantage over a hard disk if your home catches on fire.