The problem is that Linux has memory overcommit and it will OOM when a process faults a page in, not just when someone allocates memory.

So the OOM condition can hit any random process, not necessarily one that just tried to allocate. If you don't have some sort of selection, then you would still have an OOM killer, only it will be killing completely at random.

That's true, but critical processes could mlockall() after setup, so their stuff never needs paging in.