I think maybe one of Haist's concerns about uneven continuation of development with a water bath instead of stop is unevenness in the time it would take the water to mix into the emulsion to dilute the developer, not just the pour-in time, but this is a total guess. (For dilution you need some large number, say 10-20 units of water to contact each unit of developer, but for altering the pH you only need of order 1 unit of stop to reach each unit of developer.)
My Kodak (USA) Reference Handbook from 1946 discusses acid stop baths with the conventional reasons for use, and also gives formulae for SB-1 through SB-5 - includes acetic acid, chrome alum, and hardening stop baths. It has formulae for developers and fixers, but also an extensive list of which chemicals are sold in premade packets or containers, so that was already common practice in the US in 1946.
I learned to use acid stop bath when learning in the 1980s from Kodak manuals, books, and older relatives. I don't think I ever heard that there were pitched battles over stop bath until the internet.