Actually, shaded pole motors are used in variable speed fans. A popular - I would say dominating - brand of bath-room fans in our part of the world (and probably all over the world) use shaded pole motors. And that brand has a variable speed option that works just as described, by stator voltage control with a "dimmer".
This is not against the laws of nature since a shaded pole motor of this size is such a poor motor that it already has a rather high slip and this slip is very voltage dependent. A speed range from 25 to 100 percent is a very real possibility and the resulting air flow goes with speed squared (I think). The non-linear speed/torque curve helps establish stable operating points depending on voltage applied.
There is no danger in reducing the stator voltage with regard to motor heating. The losses are around 70 to 80 percent at full load and reducing the voltage only reduces total power, i.e. mainly the losses.
The only thing that one should be careful with is that a triac has an unsymmetric characteristic and this can lead to firing on only positive (or negative) half-periods, which applies a DC component to the motor - which it cannot take. The usual reaction is letting out the magic black smoke and after that - silence.