wood always moves, as your cue goes itno different environments it is always either taking in or giving off moisture. no coating will ever prevent that but the coating and case help reduce sudden changes. most roll cues on a pool table because that's what they have but the cloth isn't helping, easier to see with a strong light behind it and on a hard flat surface. Straight is an infinite measurement. Its limited by your ability to measure in an accurate way. Its possible to mount a cue between centers and turn it and check the runout. Thats a way of quantifying it.
an easy way is to stick a thcknes of paper under the gap whule it lays ona hard flat surface. If you cant' find a place where you can stick a rolling paper under it and pull it out without the cue bearing down on it you are very close. You can see what's the thickest paper that slips through the gap without resistance, That's a way to quantify it without a lathe but with access to a true surface.
I'm a self taught machinist so of course I am familiar with runout, but I dont understand the meaning of the term "taper roll"
there is another factor here, the wood is never the same weight everywhere.. You can also be concerned with balance if you want to go that far,, Like is often done with high speed machine parts it can be balanced,, It's possible to check the balance but I don't think it proves much other than a comparison. if the balance of some were more consistent it probably relates to future warpage even if it is straight now.
you might have dense wood on one side and less dense wood on the other side and that would also be an inconsistency, and it's different from runout.
you can also look at balance end to end. If it's two pieces you can also spin them separately and examine the balance of either or as a unit, as they will both have different heavy sides.. a comparison is a cars driveshaft, its balanced to a tolerance in factory and if you were into racing you may choose to take and balance it to a higher threshold.. of course the function of a cue is not to spin but that sort of balance is a way to check or define consistency.
I think if youwere to take any cue and start crushing it by putting pressure between the tip and butt. before it broke, you'd see it start to bend. If you were to mark that spot and then try it again and again you'd find the cue bent the same way each time.. when you take a shot there is some degree of whip or deformation. one could do a study of several cues and find how much pressure it took to get , lets say 1 mm of deflection under compression. the more consistent cues, take a higher amount of pressure to deflect that cue 1 mm as compared to others.. a cue with more bend will display a lower amount of end to end compression the deflect it 1 mm than a straighter cue.
personally Im not at a level of play where I;d even consider these things but if one were shopping for high end cues , there are ways to quantify all these things that can be measured.
I sometimes work in an engineering lab where they have machinery that can crush and break things and they map put a graph showing pressure over time and the failure in terms of deflection to the breaking point. they can deflect huge beams, break fasteners and measure the fail point, this sort of testing is how we go about establishing things like bolt standards and stress formulas, how much weight a structural component such a a beam can take before failure. That equipment could be used for such measurements.
since wood is inconsitent it stands to reaso that if you ahve more dense wood on one side and les dense on the other, sure you can take that stick and turn it "perfectly" true, now wait 20 years, store it perfectly ,, Next the cue is bent because of the wood aging and it's internal shrink rates are different from one side to the other...
I think thi shappens to all wood cues. turning them straight is the easy part, Making them remain straight is yet another thing.