I would suggest that for many, many players the issue of whether or not the string touches the fretboard is moot or, at best, a technicality. I have drawn two images to hopefully demonstrate the point. An incline, or slope, is formed by the string spanning the distance between the nut and the saddle above the fret wires.
To "fret" the string one must merely alter the incline so the string touches a fretwire as opposed to resting on the nut. How hard one continues to press after the string has touched the fretwire is entirely up to the individual. Pushing the string all the way down to the fretboard is perfectly allowable and legal, albeit totally unnecessary. For some there is little, if any, perceptible difference between simply fretting the string with the minimal force necessary for it to sound clearly without buzzing and pressing the string all the way down to the fretboard. For others, there is a chasm of space beneath the string that shall not be entered into. I would propose that the taller the fretwire, the more exaggerated the issue. I would also propose that this can, potentially, become more of an issue the farther one traverses up the fretboard.
We are talking about distances measured in 1000ths of inches and, if one thinks in terms of sporting events and considers that races are won and lost by teeny, tiny amounts of distance, it may be easier to see that, for some, the "technicality" is actually quite significant. Put another way, if I am driving my car to the store and back, I may or may not drive with the same level of precision, attentiveness or responsiveness as if I were driving in a championship race. For the player, there is an undeniable level of precision and accuracy that is achievable with the acoustic guitar. Just how practical or realistic it may or may not be to pursue that level of skill is a question that each one will answer, individually. Thankfully, everyone doesn't have to be an Olympian in order to enjoy the guitar.
Regarding the fact that string intonation is altered by depressing harder than is needed, you admitted, "...they do go out". That is a true statement, as any stretching of a string affects intonation. Minimal stretching affects intonation minimally. You also said, "...not always radically or unacceptably". That may be the most significant statement I have read on the topic, as it beautifully demonstrates this issue is entirely subjective. Those who have perfect or near-perfect pitch will not only *hear* the sharper notes caused by over pressing the strings, but may react to the condition as though they are listening to fingernails scratching across a chalkboard. Others will simply not hear enough of a distortion to care, or will not be interested in altering their entire technique to address an occasional pitch difference.
Regarding the role of the capo in altering intonation, over-tightening a capo will cause the strings to sound sharp, just as under-tightening it will result in buzzing strings. Some people are not bothered by buzzing strings. For others it is a horrible condition to be avoided. Tightening the capo "just enough" to make solid contact with the fretwire is a bit easier than trying to determine if the strings beneath your fingertips are actually making contact with the wood. An interesting note here is that if you really crank that capo down in order to bend the string all the way to the deck, and then fret your notes by pressing hard, hard, hard into the fretboard you have, in effect, doubled the amount of intonation alteration...your notes cannot help but sound sharp. Nothing right or wrong about it, it is just the way it is.