What do you think it should do?

I think it should attempt to verify that an answer is
(a) mathematically correct
  and
(b) in an acceptably simple form.

He thinks  (I am guessing here...) that it should compare the output
string of
a command being tested to a pre-determined computed result.

The difficulty with Stein's view is that some results depend on
irrelevant factors
such as the sequence of tests.  For example, calling Maxima repeatedly
may
increment counters for "dummy index names".
So inserting a new test can cause a subsequent one to fail.

Re-setting index counters can also make tests fail.

Now sometimes answers change.  e.g. the form of the result of an
indefinite integration can change, as can its actual value (since
there may
be a different implicit constant of integration.) or it may be
simplified better
or worse.

Many global settings in Maxima can change the form of results, as
well.
e.g. powerdisp, logexpand, fpprec,

Stein's version of doctest is too dumb.  My proposed version is
probably
too hard (being, in general, not computable, as are so many advanced
computations that need to be simplified over "all mathematics".)

So what to do?

Consider this an attempt to get sage-flame back on track, too.