Thermostat, “Ice would also affect the angle of attack vane just as it would the pitot tube”.
Not so for ice crystal icing – probably a significant feature in AF447.
Ice crystals would more likely bounce off an AOA vane (as for wings etc), because there is little forward facing heated surface area to give partial melting, a requirement for this type of ice to form. Also the free stream air-flow angle and particle speed around a vane would make adherence unlikely, whereas crystals being 'trapped' in a partially closed heated tube provides ideal conditions, particularly if the crystal mass flow is high.
Conventional icing appears to be well contained by existing pitot heating.