A good backup strategy involves reading the tapes back on a fairly frequent basis to make sure your tapes are still readable. Regardless of it's reliability, tapes do drop bits at a similar rate to hard drives at rest. You're very lucky that you have read 100% of the DAT tape without any issue (or maybe you didn't notice it, bit errors are hard to notice until you need that particular bit). Also, most companies really don't care about their data from 10 years ago (and if they do it's because they want it GONE in case of discovery).
Back then, tape WAS the cheaper option. Today, hard drive storage is on par as far as investment cost. Most tape strategies involve a large(r) tape robot and multiple heads which is where the expense comes in (also energy costs). With hard drives that is less of an issue and hard drives can also be spun down. Hard drives are also better at random access which is generally what you'll need when restoring day-to-day backups. Massive failures are usually not the problem, backup restoration usually boils down to that user wanting to get a version of that Word document from a year ago but they forgot what it was called back then. Reading through a tape for that kind of stuff is SLOW to the point of being infeasible.
Tape backup is still a good solution but it's being outgrown because hard drives are faster and for most people what it can provide is 'good enough'. Tape is great if you have so much data that you need it because of the density (a rack can hold 100's of PB worth of tape but only ~5PB worth of hard drives).