There is a hidden assumption here, one that is the crux of the problem. One thing to understand is the purpose of a “master” tape. In principle it is the final artifact that is used for reproduction of the recording. You send the master tape to the pressing plant and they use it to directly cut the “master” disk. (The master disk is a playable thing - although being cut in wax it is easily damaged. The master is plated and a “mother” is created which is used for actually pressing the records.)
The issue is, that LPs do not play distortion free. They have a range of distortion artifacts and restrictions on what can usefully be recorded on them. A trivial example is that you can’t record out of phase low frequencies with much amplitude. Doing so will simply bounce the stylus out of the groove. Luckily most people don’t want to do this, but it one reason the kick drum is mixed dead center. But there are many other issues. Mainly the LP is far from linear. Every part of the process introduces distortion and anomolies. The wax the master disk is made from has plastic flows and hysterisis that cause compression and various distortion issues. On playback the vinyl itself has some level of flexiblity, and the frequency response of even slightly worn vinyl is rolled off.
The LP process makes high frequencies very hard to record successfully as they have a very very tiny amplitude wiggle in the groove, and bass frequencies have an absolutly huge wiggle, so there is a standard compensation applied which reduces the amplitude of the bass and increases the amplitude of the high frequencies during the cutting process, and your playback system applies the inverse, in order to get the correct freqeuncy response back. (This is the RIAA equalisation.) By itself the RIAA equalisation is benign, but in combination with the other distortion mechanisms it may become less accurate and hard to control.
The upshot is that the LP process doesn’t get you back the same sound as you put in. If you compare the real master tape with what the LP plays back, they sound different. So engineers mixed down to the master in a manner that experience told them would compensate for these issues. Indeed, more than compensate for, one might argue that the addional warmth inherent in some of the distortion products became part of the desired sound. The result is that the master tape may be mixed to sound slightly cold, clinical, and a bit strident. The LP process providing just the right amount of high frequency droop and warming up of the sound to sound right.
So now you get to play back your CD which is a distortion free, flat frequency response version. And you complain that it sounds cold, clinical and strident.
Another issue was that many CDs were taken from second or third generation masters (the actual real master always being far to precious to let out of the studio) and whilst they were OK for LP cutting, limitations in their reproduction may have become more obvious on CD.
Mastering has changed over the years. In the age of the LP the master was what the recording engineer created. Now it isn’t. There is a seperate mastering step, usually (and prefereably) done by a diffferent engineer, who takes the mixdown and applies what amounts to sonic tweaks to make it sound good. These are done to the stereo tracks, and are usually careful tweaks to frequency balance and careful use of compression and levelling. The sad thing is that often the use of compression is anything but careful. The idea (if not the practice) is that the recording engineer creates a perfect a HiFi sounding track as he can, one to be listened to on the $20,000 studio monitors in a perfect listening room, and the mastering engineer creates the version that is best suited to the reproduction chain. Sadly, often the reproduction chain is defined to include a car stereo or a cheap radio, and the mastering engineer does what he is told, not what is best.