Frets, fretboard edges and playing action
Playability depends upon the convergence of neck relief, action, string gauge and tension.
Guitars respond in unique ways to these and achieving the optimum set-up for a particular instrument involves balancing these with the individual owner's playing style.

Frets really ought to be uniform, level and polished, firmly seated and be smooth-ended. This is the most significant factor in achieving a (very) low action - no matter how straight the neck is, it will only be as flat as the frets allow. You will immediately be able to feel the difference when you've had a fret polish - your rewards begin with smooth bends and effortless vibrato…
You will often find on older (much played) instruments that the edges of the fingerboard are rounded over - indeed, several 'name' re-issue guitars feature a fretboard with what is described as a 'rolled edge'. This simulates years of being handled and makes a neck feel really comfortable. You may find, particularly on instruments with a bound fingerboard, that the abrupt change between the neck and the fingerboard actually causes discomfort when playing for an extended period - the 'rolled edge' provides an immediately noticeable improvement for some styles. It might not be for you, though if you like your stuff looking like it's new-out-of-the-box, as it's a more organic-looking subject than a machine edge.

No matter what kind of action you prefer, be it ultra-low or bitey-high, the best way to achieve it is through a balancing act between bridge height and neck relief (assuming that the frets are good).