I indirectly work with forklifts, the biggest issue I can see is that they tend to be hydraulic lifting, and gravity descent, which may not be ideal, and there may be issues with the y direction stability if it's single sided, depending on the overall mass. the concept has possibilities, but fork lifts by their nature and because of safety are usually massively over engineered in the mast area, to make sure that nothing is going to fail even if somewhat overloaded. A triple lift mast, which is the normal for higher lifts, will also flex forward at higher extensions due to the tolerance of the bearings, it's not much, but for the accuracy needed for printing, it will be an issue, it might be possible to overcome it in firmware, but that's then another variable that has to be calculated and allowed for across the entire travel range.
Some of that play is taken out by rubbing strips, which will add in friction, which is not ideal, in a forklift, it doesn't matter, but again, for a printer, that's not ideal, as it might also then cause problems with the descent phase. A 3 stage lift mast has a lot of lift chains so that all 3 sections lift proportionally, but only after the first stage has lifted completely, which is related to being able to operate inside containers without hitting the roof, which is a complication that would not be needed in the same way for a printer. The other issue then would be that the hydraulic cylinders are multi stage, so there would be some challenging issues with the stepping of each stage of the ram, especially over the transition
So, while the concept has possibilities, I suspect that there's going to be easier ways of achieving what you're looking for
Some of that play is taken out by rubbing strips, which will add in friction, which is not ideal, in a forklift, it doesn't matter, but again, for a printer, that's not ideal, as it might also then cause problems with the descent phase. A 3 stage lift mast has a lot of lift chains so that all 3 sections lift proportionally, but only after the first stage has lifted completely, which is related to being able to operate inside containers without hitting the roof, which is a complication that would not be needed in the same way for a printer. The other issue then would be that the hydraulic cylinders are multi stage, so there would be some challenging issues with the stepping of each stage of the ram, especially over the transition
So, while the concept has possibilities, I suspect that there's going to be easier ways of achieving what you're looking for