I've always been under the impression that, in standard English, "replace" is only paired with "by" in the passive voice, and that "replace with" is the correct active counterpart of "be replaced by":
It can be replaced by a new one. (Right)
We can replace it with a new one. (Right)
We can replace it by a new one. (Nonstandard)
All the related discourse I can find seems to agree that the active "replace by" is unidiomatic.
However, I've noticed way too many counterexamples over the years to ignore. I'm talking about technical papers, textbooks, and the like—definitely not limited to uneducated or unscrupulous writers. The following slide from a lecture is just one typical example.
Why is this? Is there any documented rule that says this is acceptable in some category of technical vernacular? Why is it so common, yet so rarely talked about?