I know this question sounds completely subjective at first sight, it even triggered the automatic "The question you're asking appears subjective and is likely to be closed" alarm, but please read further.
Action is the distance between the fret and a string at any given fret (in fretted instruments). Normally at the 12th fret, but some instruments have less than 12 frets, so the convention might be at the 10th fret for other instruments, or any other fret really.
"What's the best action" is completely subjective under most contexts. The lower the action the less force you'll need to press the string, but the more likely it is to buzz (touch a fret you are not fretting). It can also change stuff like tone and loudness (I don't know the actual acoustic basis of these changes, but that's for another question).
So the best action is the best balance between ease of play, good tone, good loudness. This is completely subjective, until you reach an edge case: action that is too high. If you can't finish a song, or a full performance, or get too tired, or feel too much pain, then you can say, objectively, that the action is too high.
If you are not using amplification, high actions might be more fitting. Or low actions for old guitars, or some specific guitar tones. Maybe a middle ground for recording. Some don't care, most will notice immediately an action that is too high.
And that can be a big game-changing problem. Sometimes you just need to make the gig / recording happen with someone else's instrument. Sometimes you are just playing an instrument you are not proficient at, but the circumstances called for it (last-moment changes in a band you direct, a favor, you are drunk). Maybe your hand is tired. Maybe you have less calluses than two months ago. There's an endless list of situations where action can come back to bite you, so knowing how to minimize its influence seems like a very useful tool.
That's where "On instruments that use frets, where's the best spot to press a string on?" stops becoming subjective. If said instrument happens to have too high an action, if it's high enough, you can risk not only fatiguing your hands and fingers before you can end the first song, but there's high potential for injuries and pain, both short and long term.
So, where can the string be pressed, so the least amount of force needs to be applied in order to touch the fret? Barely touching the fret is not enough, but maybe we can oversimplify that one? Or is calculating the exact extra force needed in relation to the force being applied with the strums / picking needed? I guess another way of viewing it is, where between the frets is there less string tension while pressed? Is it near the sharper part of the fret (assuming a non-ideal fret that has mass)? Or near the flatter part of the fret (sharper part being the one pointing towards the side in which pitch increases, flatter being the opposite direction)?
Or is it in the exact middle, between the frets? If it's not, why is it less tension near that fret, and not near the other, neighbor of the same string? There must be an actual objective, measurable, repeatable way to answer this, right? One that can use to optimize our technique, even if we are not struggling with action (that was just one example of many where this info would be very valuable).
Another situation where this is objective, relevant, and has the potential to prevent injuries, is in instruments and fingerings where stuff like "half barre" is used, like a barre chord but you need to let some strings that are located below the barre finger sound, so you need a kind of bridge shape, making your fingers do bends that your classically-trained teacher will faint at. Putting so much force on a finger that's so weirdly collapsed is a no-no (some try to prevent collapsed fingers at all). But for instruments where non-ergonomic positions are the norm, knowing exactly where to put that finger can make all the difference.
In other words, how can we know exactly where to press a string in order to apply the least force possible to reach the fret?