About 17 years ago, I started using a stop bath after first developer in the C41 process. I was informed by quite a few people that using just water would be more than alright, I was being fussy they said.
At the time, I was processing quite a lot of Kodak Print film, which was designed for turning a colour negative into a transparency (slide). As absolute accuracy is required to get a colour corrected transparency from the colour negative, it means that your processing has to be spot on and/or, always the same.
One of the advantages I had, was that I worked in an industrial photo lab. Deciding to check out empirically whether a plain tap water bath would arrest developing in all the layers, I ran C41 control strips, which had been carefully kept on dry ice. Then it was a simple matter of getting the lab technician to run these control strips through the measuring equipment, to ascertain how close to perfect they were.
If I used a stop bath, (acetic acid) then my control strips were right on the money. If I used a water bath as a stop bath, then the control strips were ever so slightly off. It was either the bottom or top layer that was slightly off, I cannot remember.
I have used a stop bath ever since, on all hand developing processes, B&W and colour, film or paper.