I would argue “possible/potential” long term benefits, assuming the “water stop” is done badly. As an acid stop user, I would need to concede use of an acid stop is just faster and probably less wasteful of water versus replacing the acid stop with a thorough water wash (I prefer the term “wash” versus stop or rinse since that is really what it should be thought of as, and how it should be done). It could even be soundly argued if one is interested in maximum fixer longevity/efficiency/capacity ideally a typical acid stop bath should be washed out before fixing.
So there is the final answer - stop bath AND water rinse is best.

Edit: typos