  Session types provide a flexible programming style for structuring
interaction, and are used to guarantee a safe and consistent composition of
distributed processes. Traditional session types include only one-directional
input (external) and output (internal) guarded choices. This prevents the
session-processes to explore the full expressive power of the pi-calculus where
the mixed choices are proved more expressive than the (non-mixed) guarded
choices. To account this issue, recently Casal, Mordido, and Vasconcelos
proposed the binary session types with mixed choices (CMV+). This paper carries
a surprising, unfortunate result on CMV+: in spite of an inclusion of
unrestricted channels with mixed choice, CMV+'s mixed choice is rather separate
and not mixed. We prove this negative result using two methodologies (using
either the leader election problem or a synchronisation pattern as
distinguishing feature), showing that there exists no good encoding from the
pi-calculus into CMV+, preserving distribution. We then close their open
problem on the encoding from CMV+ into CMV (without mixed choice), proving its
soundness and thereby that the encoding is good up to coupled similarity. This
technical report extends a paper presented at the workshop EXPRESS/SOS'22.
