I would not depart with a faulty pitot heater, except for a low level flight in the summer.
Sure one can fly without the ASI but why chuck away a damn useful instrument even before departure? Why not chuck out the GPS while you are at it, on the grounds that one can follow roads, lakes, etc? Actually one could unscrew the yoke and chuck it out of the window also, because one can roll with the rudder and do the pitch with the elevator trim
