Regression from 7fc6e518.

This is inherited anyway.

This works because the stream output is not reentrant but it is ugly.

While there are no cases at the moment (and hopefully ever), there is
technically nothing to say that the access output must return a
constant value. By caching the value, we ensure that we will not create
an imbalance between increments and decrements.

No functional changes.

No functional changes.