The plot of the TOS episode, The Trouble with Tribbles, actually depends on the fact that a Klingon looks similar enough to humans to be disguised as one.
Towards the end of the episode, it is revealed that Arne Darvin, an assistant of undersecretary Nilz Baris, is a Klingon disguised as a human. In this position he was perfectly positioned to poison the grain on the station. This was initially revealed by a tribble who squawked when this assistant entered the room (it was scientifically verified thereafter).
Thus, there would be a problem with retroactively adding the forehead ridges -- how could he have passed for human, with such a different facial structure?
So they might not have wanted to do this. It would have damaged the plot line of the original episode.
Valorum pointed out in the comments that we see in Discovery that it's possible to surgically modify a Klingon (with ridges) to look like a human. However, Discovery came out many years after Trials and Tribble-ations, so this is unlikely to have been a consideration when the DS9 episode was created.