The ident is not a good warning of failure because it is not positive. Losing a signal is not going to wake you up like a warning tone would, or a flag. Most pilots would miss it, especially if there was something else going on that had their attention.
If you monitor the needle, you can tell it is working because it gives a consistent bearing. A needle that was stationary would attract my attention even if it was identing.
I had a Nav in a C47 tune the ADF (Radio Compass in those days!) in Auto then switch it to Antenna because that was the procedure he was used to, although in the airplane he usually flew the positions of the switch were reversed. So even though I could hear a fine ident, the needle was absolutely steady on the nose. I was feeling pretty good at how well I could fly a course until the error was picked up! It was pitch black and we were about 1000 feet below the tops of the nearby hills at the time, so it was a lesson well learned.
Many years later I was the only one of about 4 company 747s that landed in Taipei when the power failed at the airport in bad weather and the only aid still working was the NDB. The other crews were never taught how to fly the approach and they all diverted.
Sometimes the old ways still work. How long since you have done a GCA?