It might be different in mountainous areas compared with plains, but even when I specifically extend my caverns (changing the ?5? level default separations between each cavern layer to 15 levels) I rarely get the first cavern 50 levels deep, so my first impression is that this is odd.
It may depend on which world-template you go for (pocket to large), but I wouldn't really know as I rarely build entire worlds less than Large (and the non-island version of that, also, in case there's a difference between them).
The only thing I can immediately suggest is perhaps you've unwittingly punched through the topmost cavern, probably even the second cavern down, by sending your stairwell down where there just happens to be no cavern (or, like a recent fort I played, it turns out I'd happened to send my exploration stairwell straight through the middle of a 3x3 rock pillar in the middle of a cavern).
Finally, I've never yet dragged water up from the caverns via screw-pumps. For emergency/therapeutic drinking water, I've dug a set of deep wells (the method that I use having been mentioned in several other threads, recently, so I won't repeat it). Although if you're actually trying to irrigate a desert then obviously that wouldn't cut the mustard, so you have my sympathies and you probably have to do something with pump-stacks after all. Still, I've also managed to bucket-brigade from the massed ranks of wells to empty into a farm-to-be area for underground (non-soil) farming.