You have no idea what you are talking about. Most tapes are not written by people and put on a shelf. Most tapes are automatically managed by a tape library, such as this one (note that thing can store up to 900PB.) Read failures do not happen, because the library and host software together automatically count cycles and copy to a different tape when the cycles get too high, as well as detecting corrected errors and signalling when there is a problem with a tape.
z/OS, for instance, has a hierarchical storage manager where, by policy, data that is not accessed in certain period of time is moved first to slower (cheaper) disk, then to tape. Where I work, the 'to tape' time is about a month. In over 30 years of using such systems I have seen the 'DFHSM is recalling from tape' message many thousands of times, and I have never once encountered a situation where the recall failed or the data was corrupted. And the recall typically takes less than a minute.
It seems that most people on here only have experience with crappy home tape systems.
So let's do your contrasting with HDDs. That library holds up to 900PB, and uses 1.6kVA of power. It takes up 163 square feet of floor space. By my calculation, that would take over 1 million 1TB HDDs in a RAID array. How much floor space would that take? How much power would it use? How much heat would be generated?
If you have a lot of data, and do not need all of the data 'right this second', and (most importantly) have a system that can manage the data without causing the user to jump through hoops, tape makes an excellent solution. And that describes most large companies.