The very definition of high fidelity is a flat response and low
distortion. Yes, many fabulous recordings have been made on old school
analog equipment. But that equipment has lower fidelity than even consumer-grade modern digital converters.
Ethan, when you say that a person 'prefers distortion' I assume that you know that the ear/brain system converts distortion (unless outright, as in clipping) into tonality. This is why a lot of tube equipment sounds 'warm' or 'rich', because of the presence of the 2nd harmonic. But this does not have to be made by tubes in particular, solid state can do that too (the early 70's Sunn solid state instrument amplifiers are good examples, as is the old AR amplifier). Much also depends on topology.
For example, you can prevent tubes from having a 2nd harmonic simply by employing fully differential design from input to output (which is how a lot of transistor gear is designed).
Regardless, the admonishment I am offering here is to be careful about attempting to place all the 'deplorables' in one basket! The issue is that the human ear/brain system is relatively insensitive to lower ordered harmonics (2nd, 3rd and 4th) while it is **very** sensitive to higher ordered harmonics- so much so that it can detect them when often test equipment cannot. The reason for this has to do with evolution and the fact that our ears use higher ordered harmonics in order to gauge sound pressure (this fact was first documented by General Electric about 1965) and is very easy to prove with very simple test equipment (I have documented how elsewhere on this site).
So if the ear is insensitive to a certain distortion, does that mean that if that distortion is present in a given bit of equipment, that it is heavily distorted or not? This refers to a comment I made earlier where I mentioned that the audio industry tends to be about 40 years behind where it should be because for the most part it ignores how our ear/brain systems perceive sound. Certainly our ability to detect sound pressure has to be one of that more important aspects of that perception!
So where I'm going with this is that just because analog systems have more distortion to which the ear is relatively insensitive, that is not saying the same as its 'less high fi' when the succeeding art tends to have **more** of the types of distortion to which the ear is far more sensitive! In essence, as far as I can make out, digital fails because generally, while having lower distortion on paper, in practice that distortion is far more audible to the ear (which is converting it to tonality). And since this is all about stuff we hear rather than what we see on a bit of paper, I don't think its correct to say that analog is less 'hifi'.
What is more accurate is to say that analog, despite having greater distortion, more closely follows the rules of human hearing than does our current state of digital. BTW this is also true of tubes (and certain transistors) as opposed to transistors in general.
I get that it takes a bit to get your head around that 2nd to last paragraph! If you look at how stuff measures on paper, in essence the wrong things are being measured. So as a result, if the paper spec is your guide, you miss something.
This is why there is an objectivist/subjectivist debate, a tube/transistor debate and an analog/digital debate.
BTW I do not regard myself as a subjectivist- I'm an objectivist (if such a thing is really possible- philosophers will tell you that it is not) that feels that to ignore aspects of our hearing that our testing ignores is not wise.
This is why tubes and analog are still around. The market keeps it for a reason, and high end audiophiles are not that reason! They represent a tiny portion of the marketplace that keeps this stuff alive.