In the days of tape masters to vinyl master cutting, the mastering engineer had to use quite a few analog tricks to get the most 'listenable' result. But also, the character of vinyl cutters in some ways masked the undesirable character of tape. Slew rates of cutters were relatively slow, which would tend to filter out high harmonic distortion and sharp transients. Sometimes I think this is a key reason that some people find they like vinyl better -- disturbances to their beloved hearing have not been trespassed upon.
Before there were CDs, consumer digital recordings were all records. The only folks having access to digital tapes were people in the mixing booth. From a consumer standpoint, one criticism of those early 'digital' records was their 'unusual' HF balance, often described as sounding harsh, overly aggressive and possessing an unnatural high-end. But remember, they were LPs, so obviously the cutterhead was picking up the HF material captured on the original digital tape; either that, or, in the booth, the balance was adjusted in order to accentuate the highs. I don't think we can necessarily claim that highs (including all the 'bad' harmonics) were somehow 'filtered out' by the cutterhead carving the lacquer.
Most audiophiles, the ones complaining about it, probably didn't have much HF hearing to begin with, since they were older. So my guess is that it was not harmonic distortion and sharp transients that were the source of the 'problem', but simply the overall FR balance of the recording, which they found unpleasant.
My guess is also that record companies were guilty of accentuating the highs in an effort to 'push' the new technology--by showing everyone that they were giving consumers what they had always been missing. Not unlike when stereo LPs first made the scene. Some of the most weird and outrageous mixes were released, simply in order to 'highlight' the stereo effect.
As far as 'sharp transients' go? Toward the end of commercial analog (that is, after CDs took off and no one wanted to buy records), boutique outfits were releasing Direct to Disc LPs on special, imported low-noise vinyl. Some of these had remarkable fidelity, with extremely clear and detailed transient attacks, and lovely highs. Half speed mastering..., 45 RPM,... and all that. So we can't necessarily blame the cutterhead for filtering out highs and transients.
I'm not sure I understand your point about the 'undesirable character' of tape'? Certainly analog tape was/is not as 'transparent' as digital. Few would argue that, today. But analog tape was never considered undesirable per se. It got to the point that it was too expensive to use, and too cumbersome, and too time consuming; an overall major hassle to keep the machines going, etc.--so it was undesirable from that standpoint, certainly. Also, for archival purposes, analog tape is not very good. I would more argue that it is 'second best' to digits, but I would not say it is undesirable, from a strictly sonic standpoint. A lot of great recordings were made on analog tape. Much variation was/is machine and tape dependent. Obviously none of that matters with digits.
Two anecdotes:
1) Peter Aczel owned one of Mark Levinson's modified Studer A80 decks. Master tapes (and early generation tapes) played on the Studer were claimed to be better than records. I remember him discussing Peter McGrath's tapes, made and auditioned on McGrath's Stellavox. No one complained about undesirable characteristics.
2) Max Wilcox once gave Peter a DAT copy of one of his upcoming DGG releases. Peter was highly taken with the recording's overall sound quality. After the CD came out, he was sure that the engineers at Deutsche Grammophon had mucked up the recording, because he didn't remember it as sounding the way it did. Max told Peter to dig out the DAT, and conduct a level matched A/B, which he did. He then could not tell any difference between the two.
Whatever and however is was, back then, after a while folks became used to digital recording, preferring it to analog. Surely the overall product became better. I'd like to think that upstream, producers and engineers simply figured out how to adapt to their new machines, without exaggerating the sonic product in ways not helpful. Digital recording also has been a godsend to the amateur recordist. So for that, we are grateful.
Merry Christmas to all.