You generally have two bottlenecks in tape seek performance. The first is the fetch from the robot, which can take seconds. The other is spindle rate on the tape drive itself which is limited by the durability of the tape. Also, in order to make this work, you'd need many tape drives, with many robots accessing the same racks of tapes. There's a physical limit to the number of drives and robots that can generally fit in a cage and have access to the same tapes so you'll have a lot of trouble pulling this off.
All this and you still haven't addressed the difficulties involved in overwriting tape. Nor does it address the normal redundancy you already need to deal with corrupted and broken tapes, or the fact that you'll need to expand your setup even further if you want multiple users of the filesystem at once.
Current systems already do caching and concurrent reads off multiple tapes. Tape is still not a drop in replacement for disk. Any application you write for it has to have it's limitations in mind.
Considering the seek time of the robot arm. Striping data across four tapes just means you need to wait for the robot to grab four tapes.
Although brudgers talked about writing at different offsets, that's actually pointless if you don't rewind each tape between accesses (and why would you?). Assuming random access patterns, your read speed on the array will, on average, increase linearly with the number of tapes. This will come at the cost of write latency, the magnitude of the cost depending on how you implement the array.
If the array has independent drives (which would be very expensive, but let's assume for the moment), then your write latency is always dependent on the longest seek (you have to wait for the write to occur on every tape). That means that as the number of tapes increases, your average writing latency will approach the worst case for a single tape. In other words, with an infinite number of full drives, you would always have to wait for one of the drives to seek across an entire tape. That's pretty bad news, but it's acceptable for some cases.
On the other hand, if you had one drive and a tape library, your write times would really be completely unacceptable. Your linear read seek speed increase would come at the cost of a linear write seek time increase, plus a linear increase in writing throughput time.
> It's fascinating that tape drives are making a comeback, but to suggest that they can replace HDDs is just a fantasy
Tape + RAID vs. HDD with no optimizations is a useless comparison. Why would anyone even care about that?
With that said, I outlined in another comment[1] why a mirrored array of tapes would have pretty huge drawbacks regardless. Even if you have an expensive array of tape drives (as opposed to one drive with many tapes), a mirrored array will drag your write seek performance toward a constant worst case as the array grows. The same is true of RAID 1 for HDDs, of course, but the worst case seek time of an HDD is orders of magnitude less than that of a tape drive, so HDDs still win.
In any case, if you look at the details of the situation, the answer you come to is pretty boring: tape drives can compete with HDDs in a small slice of real world cases (often when used in conjunction with HDDs), and higher density tape drives will slightly widen that slice.
If you have a situation where you are writing a ton of data, but almost never reading or erasing, then high density tapes will play well to that situation (sans mirroring).
If you have a situation where you are writing a relatively small amount of data over a long period of time, reading it back comparatively frequently, and never erasing anything so that your total storage needs become very large, then maybe a mirrored array of tape drives would make sense, if it were behind a sizable HDD array. But it's a stretch.
When the data set is so large that maintaining it all online at once is impractical and the nature of the data makes continuous and immediate access unnecessary, then tape may solve the problem.
I'm not saying that future tape technologies will be as fast as the hard drives of the equivalent future - linear access has inherent limitations. However, there are relatively simple ways in which data access could be improved and such improvements (and some tuning) could make tape adequate for some applications.