YEs, since no system/speaker delivers a perfect reproduction, there is always distortion of various types.
It's the end result as a whole how that is delivered to and registers with the listener that really matters. If listening to music live sounds good but a recording at home does not, that is due to the distortions inherent in the reproduction.
Which ones matter most though and can be practically addressed, and how? That's the key. WHen it sounds "good enough", the distortions have been tamed sufficiently.
The trap is thinking that this can be achieved to satisfaction in all cases all the time via putting the right system in place. It can't. All recordings have distortions as well. Those producing the recordings play the same game as the listeners in terms of how to make things sound their best. Its all an art based on science, but not pure science. More like how to produce a Monet or Rockwell work of art through technology than a distortion free reproduction.
Amazing how well it all can work out in the end these days with modern technology! It'll never be perfect/distortion free though. The trend over time is positive though, in other words better technology = less distortion. So just learn to choose your distortions wisely! :^)