In effect, you are assuming that your uninitialized and initialized variables straddle a page boundary. This is obviously not going to be a common occurrence. In the common case you are allocating something on the heap. That heap chunk descriptor before your block has to be written, triggering a page fault.
Besides: taking a page fault, entering the kernel, modifying the page table page (possibly merging some VMAs in the process) and exiting back to userspace is going to be A LOT slower than writing that variable.
OK you say, but what if I have a giant array of these things that spans many pages. In that case your performance and memory usage are going to be highly unpredictable (after all, initializing a single thing in a page would materialize that whole page).
OK, but vectors. They double in size, right? Well, the default allocator for vectors will actually zero-initialize the new elements. You could write a non-initializing allocator and use it for your vectors - and this is in line with "you have to say it explicitly to get dangerous behavior".