[TIMTAPE]

That's true. The specific need to record at 20db below reference was usually to avoid HF saturation and the misleading frequency response results that gave.
That was much more of a problem with slow speed recordings of which cassettes were an example. Open reel tapes at the same slow speeds had the same problem.

For cassettes, Chrome and then Metal came along which performed better than Ferric specially in the HF MOL saturation area. My 90's TDK tape reference book states detailed performance figures for their range of tapes at that time. MOL (saturation output level) at 10Khz for their TDK D tape was -8.5db and for Metal -1.0db ( both re 250nWb/m)

Many Tascam Portastudio decks performed quite well in the HF saturation department. They used double cassette speed (3.75ips) and "Chrome" (Type 2) tapes.