You can certainly correct for all these errors if you are able to measure them. E.g. if your tool moves 1um down in position (x,y,z) due to the machine deflect

You can certainly correct for all these errors if you are able to measure them. E.g. if your tool moves 1um down in position (x,y,z) due to the machine deflecting all you have to do is adjust z by 1um at that point. As long as there's no other issues and the only issue is the accuracy of placing that tool you're good. One example is precision ball screws, those typically come from the factory with data for compensating the screw. The screw isn't perfectly accurate on its own but if you apply the correction data you get better accuracy. The screw isn't less repeatable because of this, it doesn't wear down faster, it's just that it's absolute accuracy isn't perfect out of the factory so they just measure that and give you the corrections (let's say on the order of 5-10um over 1m). In usage the accuracy is also a function of temperature, so you may want to measure that and correct for it... or you may use a linear encoder or an interferometer ... point is, the screw does not have to be perfectly accurate, it just has to be repeatable and the remaining error can be corrected...