Also, if the heating fails or is overwhelmed by the amount of ice accreted, the bending moment will change and it becomes just as inaccurate or useless as an iced-up pitot tube.
What about a birdstrike - if a bird manages not to take off the plate but to bend it, the cosine of the bend angle will need to be calculated out of the measurement (if the system survives).
Also, a plate sticking out in the airflow will cause drag and might cause vibrations/tones at least in a certain speed range.
Well, the idea might be crazy - but why not harness this effect? An array of plates of increasing size and therefore frequency that will start to hum at different airspeeds might be installed in the airflow. Then add a microphone that catches the sound of this contraption and a computer that translates the frequency into an airspeed for indication.
Also, why not turn the pitot tube around? Then, Ptot will no longer be Pstat+Pdyn but Pstat-Pdyn - the much smaller values are likely harder to handle but at least there is no longer an opening facing forward and susceptible to icing.