Aside from the more or less spectrally "normalized" modern pop productions, the sound of classical, jazz and others is all over the place.
This is especially true and more or less astonishing for classical, where the goal over the now about 10 decades of music recording always has been achieving a natural sound, and processing of any type was always sparse.
The reason for this cannot be simply connected to the use of a certain microphone type. There is a multitude of factors, in which the microphone plays a lesser role (although as a front end, it defines and sometimes even limits the quality of the outcome).
On the playback side one has to admit that there is no real universal reference loudspeaker (in a reference acoustic environment) or even less, reference headphones.
This is one of the biggest problems for every audio engineer: where and how will the recording be auditioned by the audience.
E.g., have a look at a typical modern (and expensive) television set: the tiny speakers are on the backside, radiating to the wall. Need I say more?