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I could be wrong here, and if so would ask John Mallinckrodt to correct
me, but I somehow got the idea that John's earlier suggestion for giving
'angle' an irreducible dimension was essentially equivalent to a call to
consider the 'radian' as a base unit (rather than its current status as an
officially supplementary, but in practice derived one). Giving angle a
dimension would have the effect of putting powers of angle in the
dimensions of quantities (and corresponding powers of radians in the
units of) defined in terms of rotations or their generators such as
torque, moment of inertia etc.. This complication would have the
beneficial pedagogical effect of helping distinguish these rotation-based
quantities from other ones (such as work and mass quadrupole moment) that
are not defined with reference to rotations.