Copy-on-write Confusion: Don't all Processes write to memory anyways?

Copy on write in the Linux kernel allocates memory for a process when it attempts to write to a page that is referenced by a different process. This is an optimization because allocating pages every time a process is forked is expensive. However, the thing that I am confused about is that don't most processes eventually write to a page anyways?

I tried to learn about processes that never write to a page but I could not find any examples.

Remember what is probably the very most common use case of fork(): in combination with one of the exec() functions. Since there is usually only a few lines of code in the child between the fork and the exec, it will likely only write to a very small number of variables, thus touching only a small number of pages. Those pages must get copied, regardless. But the vast majority of pages will not be written by the child at all, nor will they be written by the parent in the short time window between fork and exec. (Keep in mind that the parent is often doing wait() in which case it is also touching very few variables.) With COW, those pages do not ever need to be copied.

When the child does exec, all its memory mappings are destroyed, and the new program is mapped in their place. At this point, the memory of the parent process is no longer shared with anybody, so the kernel can set it writable again, thus allowing the parent to use it without triggering any copying.

So COW has the effect of making the common case of fork/exec much more efficient, without breaking the uncommon case where the child does do something nontrivial. And even in the latter case, there is still some savings, because it's likely that the parent and child aren't going to touch all of their pages.