What about a design change: connect the closed end of the Pitot tube to a high pressure pump. Whenever erratic air speed indications are suspected, push a burst of fluid via this connection to dislodge ice, dirt or leftover scotch tape.
I don't think that would be a workable solution. The amount of pressure required would be enormous in the case of a solid blockage - especially a plug of ice.
I once had to replace a pitot tube on a Bell Jet Ranger helicopter which was completely blocked. We suspected that the blockage was caused by an insect.
The maintenance manual specified that a maximum pressure of 20 psig could be used to attempt to purge a blockage (after disconnection all downstream sensors). We tried the procedure, without success.
It turned out that the tube had been blocked by a mud dauber wasp, which had built its nest within the tube over a 5-day period that the aircraft had been parked outside (in mid-summer) with no pitot tube cover installed.
Once the new tube was installed, we connected a regulated nitrogen tank to the old tube to determine just how much pressure it would actually take to clear the blockage.
We had to apply almost 200 psig of pressure before the wasp nest finally dislodged, and when it did, it came out like a bullet fired from a rifle.
The point being that trying to remove a solid blockage from air data probes with reverse air pressure would only be likely to cause major damage to the probes themselves, or to the associated plumbing - to say nothing of the extremely sensitive sensors to which the plumbing is attached.
JR Barrett