Let's think about this from a physics/chemistry/engineering point of view, focusing first on the rationale for using stop bath and then on whether there are alternatives to accomplishing the same end. I am hearing two reasons presented for using stop bath, one is to stop development "right now" and the other is to preserve the fixer. The rationale for stopping development "right now" can be broken down into two components., One is to assure known and repeatable development times. The other is to assure evenness of development across the film (or print).
Let's look at the issue of known and repeatable development times. The termination of development by acid stop bath is controlled mainly by diffusion of protons into the emulsion. This overwhelms the buffer, lowering the pH, which stops development. Developer also diffuses out of the emulsion, but this a slower process that is not rate-controlling.
Termination of development by water instead of stop bath is also controlled by diffusion. In this case it is diffusion of buffer and developer out of the emulsion. As buffer diffuses out of the emulsion the pH drops, and this will slow development and ultimately stop development once the pH drops enough. (Most developers don't work at pH 7, which is the pH of pure water.) Simultaneously, the developer also diffuses out of the emulsion, and this also slows and ultimately stops development. The molecular weight and physical size of molecules of most developers is larger than that of most buffers, which implies that the diffusion rate of buffer is faster than the diffusion rate of developer, so buffer diffusion is probably rate controlling, but in any case, both effects act in the same direction, so the fine points are not that important. (For you chromatographers out there, there are also fine points about how affinity of gelatin to developer and buffer molecules affects the rates of transport, but that introduces another conceptual layer that does not really affect the final conclusions.) While these processes are occurring development continues to occur, though at a reduced rate. This means that development continues longer if one uses water than if one uses an acid stop bath. However, diffusion is a pretty reproducible process, so the net effect is to simply increase the effective development time. It would be easy to compensate for this effect simply by decreasing the development time slightly. I am not sure how much one should reduce the development time, but I would be very surprised if it were more than 15 seconds.
With regard to evenness of development across the film. That is going to be controlled by whether or not the full surface of the film is exposed to the stop bath (or water) at the same time. Unless there is a big difference in solution viscosity of pure water vs. acid stop bath, this effect is going to be the same, regardless of whether one uses stop bath or water, so evenness of development should not be affected by the choice of acid stop bath vs. water unless there is some other unaccounted for effect taking place.
The final conclusion I make is that it doesn't matter if one uses pure water or stop bath, provided one makes a slight adjustment to the nominal development time to account for the difference between acid stop bath and pure water.
As far as preserving fixer is concerned, an acid stop bath might have a very small effect in preserving fixer compared to using a pure water stop bath, but a pure water stop bath will remove the vast majority of buffer and developer before the film is transferred to fixer, so in this respect the difference between acid stop bath and fixer is unlikely to make any difference. However, if the film is transferred directly from developer to stop bath then fixer depletion could be more of an issue. In any case, this is really more of a practical economic issue than anything else, i.e. how often one needs to replace the stop bath.
The above analysis is based on theoretical analysis of the physics and chemistry of the process and how these impact the engineering of the process. The ultimate test would be controlled experimental studies. However, I am not planning to do the experimental studies because I am satisfied with using water as a stop bath. Nevertheless, I would be interested in the results if someone else wants to do the studies.
Correction: Where it says "i.e. how often one needs to replace the stop bath." it should say "i.e. how often one needs to replace the fixer."