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Correct, it increases the error slightly, but not much.  It's already fairly imprecise.  Users won't be affected by this imprecision unless they're opening multiple tabs simultaneously, in which case we can safely say they're on multiple pages; there's no benefit to choosing one over the other.

The cost for maintaining the existing veil of precision isn't worth it.  It necessitates a lot of locking and writing on high-traffic sites.  Most sites are going to solve that by ignoring it or scaling vertically instead of resolving the underlying issue.