milsabords
Pitot tubes can be clogged by dust, water or ice cristals because air flows inside from their inlets to their drain holes.
I imagine a tube w/o a drain hole, fed from the aircraft by a variable presssure air pump, controlled to deliver a fixed air flow. The internal pressure is a function of the outside total pressure at the tube inlet, therefore the air speed can be measured.
Side benefit: a simple test on the ground can detect clogging by insects or scotch tape.
Only problem with this concept is that what happens to the water droplets that inertially fly through the outflowing air at the pitot inlet and accumulate.
The existing holes appear able to clear the water out of a full tube in 2 to 4 seconds at 270 knots based on an experiment I did last year with an old airline style pitot tube.
The better solution is to actually monitor the outflow of the tube drains, as suggested by JD-EE. The technology to do this exists. Loss of outflow means the tube is producing invalid data.
With that information, you could crank up the heat in the tube to a very high level and send information to the system to disregard that data for the event duration. And if the fault persisted (bug in the hole) send an ACARS message to get it fixed. That way you don't keep flying with blocked drain holes.