On the timing issue:

Notation is a limited way of transcribing music there are many things it simply does not describe - the volume of individual notes for example, its a limited system, developed ad hoc from a variety of choral and orchestral needs - over centuries and for the limitations of scratchy quills on bits of parchment.

I once saw a chart for a sax solo (pick up the pieces) which was a mess of hemi-demi- quavers (64ths US i think. What was really going on was the player was playing a little early thats all. If you wrote it out without the 'earliness' it became legible and simple to play. Similarly a live performance scored by a machine will capture nuances in a unwanted pedantic and over scrupulous fashion.

There are two forms of quantise (in my mind at least) with variants of each. In 'ordinary' quantize the length of the MIDI notes are adjusted and so the nuances of the performace are lost (you can keep two copies of course).

In the second type "Display quantise" the length of the MIDI note remains the same (and the performance left untouched) but the notation is adjusted to 'make sense' or simplify it for others to read. Cubase uses this tech but I am not sure about FInale or Sibelius. I think not, but dont know.

Capturing melodic ideas from a performance has two aspects. Firstly capturing the actual sound. Secondly, making some form of non-acccurate notational representation - a simplification - that is easy for a reader to intepret, particularly if sight reading. These are two different tasks. Notation should be simple as possible (IMO) and the musician should add the nuances.