If you look at this video showing the production of Channellock pliers/wrenches, at about 3:48, you can see one of the workers touching up the jaws on diagonal cutters.
The tool he’s using sort of looks like a file, but it may be a rectangular bar, presumably with abrasive paper or paste applied to it.
Presumably it is possible to touch up diagonal cutters that are just a bit worn, although it would require the right touch and patience and experience so in most cases it would just be easier to purchase new.
With Channellock, one other advantage is they use a Cutter and Anvil design, which may make it easier to match up the jaws.
I don’t know whether they’ve always used this design, or whether it was more recently introduced.