Why not use GT2 en lieu of a Z-axis threaded rod or leadscrew? Having just re-read Tom's excellent answer to my question Advantages of GT2 over a rack, as my comment ponders1:

Why is a threaded rod, or lead screw, used for the Z-axis movement in a Prusa (and its derivatives) given the inherent problems relating to backlash?

Indeed the majority of, if not all, delta printers generally use GT2 for the three vertical movements, presumably for this reason (of reduced backlash). Maybe cost and simplicity also play a part? I am purely speculating on these three reasons. The mass of the three vertical carriages and the associated carbon rods, would certainly seem to be a lot less than the mass of a cartesian X-axis gantry. 

Is it purely for reason of the mass of the X-axis gantry (especially if the extruder is mounted upon it - in a non-Bowden solution) that mechanical rods are used, as GT2 would not be able to lift the weight, without stretching (both over time and flexing slight upon each movement)? If so, then surely wire reinforced GT2 could be used?

As a potential aside, would another consideration be to compare the inertia of a GT2 solution to that of a threaded rod, leadscrew solution2?



1 I have a nagging worry that I have already asked this somewhere else, but after having spent the best part of a day looking for it and failing, I am asking here.

2 Although I am not entirely sure how that would be measured/compared, as one solution (leadscrew) is rotational, with a translation to linearal via the screw thread, and the other (GT2) is (effectively) fully rotational? I am going to ask about this particular point on SE.Mechanical Engineering, and will update this question as necessary.
A lead screw can be fitted with a anti-backlash nut to get past your concern about backlash. Generally, backlash is not that of a problem considering the weight of the carriage (e.g. Prusa), or whole bed (e.g. CoreXY or Ultimaker). Certainly if you're not using Z-hop, the Z screw will only advance in a single direction!

GT2 belts are always reinforced with fibres either glass, steel or some other fibre, all with their own (dis)advantages.

As far as I have learned is that lead screws are far better capable of transporting higher loads at the cost of speed. Also, a leadscrew will have more resistance so that if you unpower the steppers, the gantry will not plummet to the bed.