Just intonation is just a theory. In practice slightly detuned intervals sound good. Imo they can even sound better than when they are perfectly in tune.
Sometimes musicians deliberately use detuning to create a sound, for instance in the "chorus effect".
EDIT: Another interesting fact is that pianos aren't actually tuned to equal temperament. The intervals are tuned slightly bigger than it would dictate, to accommodate pianos' slightly inharmonic overtone series.