I have never at a tape recorder in my hands that would go above 20 KHz. That was a struggle even at 15 ips with 1/4" tape and 1/8" track width.
Tape heads were also limited in the bass. Only Studer heads can reach 20 Hz.
"Limited" in the bass to about 35 Hz at the highest speeds. As speed drops the LF limit drops. If you needed 20 Hz, your dropped a speed and carried on. Well after digital took over the pro recording space, the studio's tape deck was still pencilled in for laying down drum tracks.
Cassette decks with metal tape had -3dB points of 22KHz.
STUDER and MCI studio decks recorded at 30 IPS, not 15 (which is a consumer standard), on 2-inch wide tape. Of course they manufactured decks for a variety of users, right down to open reel machines at 15/16 IPS (so-called "loggers") which were used by radio stations who were required by law to keep a record of the broadcasts, and by police in surveillance.
I spoke to the STUDER rep at the Western Association of Broadcast Engineers convention in 1977, who proudly told me they had just sold 35 logger to the RCMP in Regina (Sask, Canada). At the time wiretapping was illegal in Canada, and would remain so for just over a decade (after a scandal involving, in part, RCMP wiretapping of Quebec separatists).
Dolby NR (studio grade, not Dolby B or C) and DBX noise reduction was routinely used in recording studios going back to the 1970's (1960's for Dolby), a record level of 45dB resulted in a S/N of 90 dB, and significantly, enjoyed the frequency response and headroom (freedom from saturation) of a 45 dB record level, -20dB from the 0dB point, which itself is about 10dB short of the saturation point, and the frequency response standard in magnetic tape decks. In other words, meeting the spec.
The TEAC A-860 (pictured, above), a deck I have used, with 1/7/8 IPS and ⅛" tape with a track width of 1/32 inch had a specified 20Hz~20KHz frequency response at -20Vu (the cassette measuring standard) and 90 dB SNR with DBX at -20Vu. I measured this deck; it easily exceeded spec.
The TEAC C1 MK II, another cassette deck, has a specified frequency response of 20 to 22 Khz out of the box.
What do you suppose a STUDER with 2 inch tape at 30 IPS could achieve? All STUDER open reels are specified at 0Vu at 30 IPS, -10Vu at 15 IPS, and -20Vu at 7.5 IPS (the same level cassette decks are spec'd at).
From a test report in Modern Recording and Music magazine, using half-inch Maxell UD XL II tape (normal bias, and not the AMPEX 456 the unit was calibrated for and the tape used in recording studios almost exclusively) on a STUDER B-67 (1978):
"In all cases [whether measured at 7,5, 15 or 30 IPS) frequency response was ruler flat to well above 20 KHz" ... "outstanding 77 dB SNR" [without any NR]. Note that STUDER's specs are 40 Hz to 20 KHz 30 IPS 0Vu and SNR of 71 dB, extremely conservative, which was their practice.
Measured frequency response, Maxell UD-II tape; ½"
37Hz to 24.5 KHz, +0/-2dB, 30 IPS at 0Vu
23Hz to 24.5 KHz, +0/-2dB, 15 IPS at -10Vu
16 Hz to 21.5 KHz +0/-2dB 7.5 IPS at -20Vu
At -20 Vu and 30 ips with DBX NR, these decks were known to have a -2dB point in excess of 30 KHz at -2dB and better than 90 dB SNR.