Moving data from one process to another by messing with the MMU state to move a page from one process to another has been tried. Mach did that. Unless you're moving megabytes of data, on modern CPUs, messing with the MMU state is usually a lose. Caches and translation lookaside buffers have to be flushed, which is worse than copying. Copying is a cheap operation on most modern CPUs, because the data paths are wide and the data you're sending is probably in cache. Also, the data has to be page-aligned for this to work.