Fron
Could it not be designed to deploy when all 3 pitot tubes disagree simultaneously, or on the command of a pilot who has an intuition that something isn't right? Is the pitot tube system prohibitively expensive?
Expense is not a decision gate here.
Measured reliability is the issue. The more systems you add the less reliable you are (less safe).
The typical design decision here is to have a backup that gives up on trusting screwy readings and still flies the aircraft. Else one would have to roll some dice to pick which reading is correct. I don't for an instant trust yet another probe with way less than 100% relibility (it only gets used once in a lifetime) that is expected to solve a unique problem.