Low Action - It's not all benefits
If you play both classical and electric guitars then you get used to the fact that the action on most electrics is far lower and easier than it is on even the best classicals. The most obvious reason reason for this is that there are is a basic trade off between action and maximum volume. To get more volume out of the electric guitar you turn up the knob. You don't typically pluck twice as hard with your plectrum. On the unamplified classical guitar however, your volume is controlled by your playing action. Although your maximum volume is a fraction of that of an amplified instrument, the intrinsic dynamic range (the difference in sound intensity from the quietist) to the loudest is far greater. You use technique to exploit this dynamic range - from your finger muscles, the muscles of the hand, wrist and even the arm can be brought into play.
But as the volume increases, there is a limit at which clear tones get muffled by unwanted noise. The lower the action is set, the sooner unwanted noise from strings hitting the frets comes into play. Depending on the style of music, this can rapidly become intolerable. Playing Dowland it becomes intolerable far soon than it does playing Flamenco and the Flamenco guitar is generally set lower then the typical classical as playing speed is prioritised and the instrument is generally played in an ensemble where there is a great deal of competing noise.
Action and string tension are also related. The rule of thumb is that the lower the action, the higher the tension of the string. When your instrument is made of fine woods and glue, you do not want string tension to go too high (it is amazing how high it goes anyway!). It is different on a solid guitar where the bridge is bolted to the body and the neck secured by a metal rod. Action can be lowered and tension can go up. As I understand the physics here - feel free to write and correct me - the string with the higher tension has a lower amplitude (that is less physical vibration). That means it is less likely to hit frets when you are playing loudly.
But back to the question at the top: there is a general sentiment that low action is better than high. The classical guitarist however needs to have the skill and technique to exploit the low tension. If the angle of attack of your right hand (plucking) finger nail is more upward than across the string, then there is more chance of the string hitting the frets and causing noise. I find too that on instruments with very low action, it is that much more important to be accurate in the placement of your left hand (stopping) fingers behind the frets. Some instruments will tolerate your finger stopping strings several millimetres behind the fret. On instruments with low action however, I find that this tolerance is much reduced. For some reason this always seems most noticeable when playing the D4 string on the lower frets. If your finger strays too far behind the fret, a strange distortion creeps into the note - not quite a buzzing, more an unpleasant interference. I am sure more experienced players could say a lot more about both right and left hand technique. I'm sure too that the teachers will say there is nothing new here, just the kind of good practice they are at pains to impart. But for many of us, bad habits creep in over the years and when you move from the an aging but comfortable instrument to a new one with lower action, these bad habits can really surface with a vengeance.