Why is a diode-connected BJT more "ideal" than a simple pn diode?
Diodes come in low-current types, that have a point-contact-like
geometry, for high speed operation.   The depletion region in
such diodes is a hemisphere, not a uniform slab, and that
deviates from the diode equation geometry.   Diodes also come in
high-current types, which often have intentional resistive
layers, in order to prevent  hot spot formation.   The resistive
features are not part of the diode equation either.

Small-signal transistors, however, have a large flat thin base
region (which is the right geometry) and minimal resistance
in the emitter, and low-resistance collector metallization,
so the junctions DO fit the equation, even if not 
specifically designed to do so.  It's accidentally
the better 'ideal diode' because of features frequently
designed into diodes.