No, there is no practical way to repair the halfnut guide. Yes, I would replace it.
Your 2nd paragraph is either incorrect and poorly worded or correct but poorly worded. It is incorrect in that it does have power feed capability for both longitudinal and transverse (cross-feed) drive. It is correct in that longitudinal drive for both turning and threading is provided by the Acme threaded leadscrew and the halfnuts. Much more expensive lathes have two methods of longitudinal drive. The lead screw and half nuts are only supposed to be used for threading because it maintains the thread accuracy for much longer. For turning, the carriage is driven by another drive shaft through a gear arrangement that is conceptually similar to the cross-feed drive. However, whether this is actually money well spent or not is subject to argument. My attitude toward the question (which would almost certainly be ignored or overridden by the sales department if I were running the engineering department of a lathe manufacturer) is that a lead screw, half nuts and the gears to drive them are almost certain to be cheaper, simpler and more reliable than the drive mechanism including drive shaft and second set of gears. So if the lead screw and half nuts need to be replaced in order to maintain threading accuracy, just replace them. You still save money. And the machine is automatically more reliable because it has fewer moving parts.
What's the problem with removing the cross feed knob?