Rather surprisingly, many manufacturers use brass or even softer metals like Mazak for half nuts and cross slide nuts. They are sacrificial, like brake pads and clutch plates, designed to wear out without damaging the mating part (in theory!). The idea is for all wear to occur on the nut, not the mating feed screw or lead screw.
A worn nut will have a bit of backlash, but will faithfully follow the thread on the leadscrew, and so will cut an accurate thread, or in the case of cross slide will still give an accurate reading on the micrometer collar. But a worn screw will have variable pitch along its length, varying incrementally from the original standard on the unworn bit to the full amount of wear in the middle of the worn section of screw, and then back incrementally to standard again at the other end.
I make my own half nuts and feed screw nuts, all out of brass. I have yet to wear one out in the home workshop. If I were forced to use bronze, I would prefer a leaded bronze. Phosphor bronze is tough/hard stuff and running on unhardened steel shafting usually leads to comparatively rapid wear on the shaft, so I would imagine the same to be true for mild steel screws.