As I understand it, developer residue itself also impedes the longevity of the fixer.
I'll let the chemists here either correct me, or explain why.
Possibly developer residue may reduce the longevity of the fixer. However, from simple chemical reasoning, acidifying the film is not likely to result in faster removal of developer from the film, so it's not likely to much affect the amount of carryover into the fixer.
It's actually not quite this simple, but acidifying the film in the stop bath will convert the developer from a negative ion to a neutral molecule or maybe even a positive ion, depending on the chemical structure of the developer and the pH of the stop bath. It does not destroy the developer, and changing it from negatively charged molecules to neutral will not likely change the diffusion coefficient very much, so the developer (in the neutral form) is not likely to diffuse out into the stop bath solution much if any faster or slower than if it were in the negatively charged form. Hence, about the same amount of developer will remain in the film, regardless of whether the stop bath was at a low pH or neutral pH. Consequently, about the same amount of developer will later diffuse into the fixing bath, regardless of whether the stop bath was acidic or neutral.
After that long-winded explanation, let me add that what I wrote above is still a simplification, possibly and over-simplification, and here's why. The time it takes for the developer molecules to diffuse out of the emulsion is probably not the same as diffusion through an aqueous solution, and here's why. The residual developer, may have some affinity (in the chemical sense) for gelatin molecules. There are dispersion forces, dipole/dipole force, ion dipole forces, and ion-ion forces that may be present between the gelatin molecules and the residual developer molecules. If so, then the developer molecules may have a tendency to be sticky relative to the gelatin molecules, and the amount of this stickiness will depend on what forces are predominating, and this is going to depend a lot on whether the developer is in ionic form or neutral form. It also depends on the acid/base chemistry of the gelatin. For example, if the developer is in neutral form, and if the pH is at the isoelectric point of the gelatin then the developer molecules are going to avoid interacting with water (which is highly polar) and will tend to stick to the gelatin. Other conditions may tend to produce different results. Hence, the diffusion rate of the developer out of the emulsion may depend on many factors that are hard to predict without additional information.
In any case, the amount of residual developer left in the emulsion has to be pretty low, and if any development occurs after the emulsion is put in the stop bath, it will tend to favor the chemical depletion of the developer more in the water stop bath than in the acid stop bath, so if anything there is likely to be less developer to transfer to the fixing solution if water is used as the stop bath than if an acidic stop bath is used, and to that extent a low carryover to the fixing solution is probably favoring a water stop. However, in any case, the amount of residual developer left in the emulsion is probably so low that it can be pretty much ignored. This is because the volume of the emulsion is a tiny fraction of the volume in the development tank, and much of the emulsion volume is taken up by gelatin molecules, which would not leave much volume left to hold the developer in the emulsion. This thought may need to be modified a bit if there is a high affinity between gelatin molecules and developer molecules, but even in this case it's hard to imagine that there is much residual developer left in the emulsion. If it is perceived as a problem then two successive "water stops" on the film would eliminate this as a concern.
Also, if one is using a water stop then a lot of the concerns that have been raised here about buildup of developer in the stop bath are eliminated by simply by not trying to re-use the water. Just use it as a stop bath in one-shot, and then discard. Water is pretty cheap where I live (less than $4 for 1000 gallons), so the cost of tossing the water after each use is negligible.
The above discussion is based on general chemical considerations, rather than a special expertise in photochemical chemistry, but if there are parts of the analysis that are wrong then they can certainly be discussed.
My credentials: PhD in Chemistry, specializing in physical chemistry. The final 16 years of my career were in clinical chemistry, which by the way is the same field where Richard Henry (author of "Controls in Black and White Photography") spent his career. In fact, he was a major figure in the field of clinical chemistry.