There are two problems with unreliable airspeed:
1. The unreliable airpeed per se.
2. The bigger problem is when the system (and the pilot) does not recognise that the airspeed is unreliable - and automation then insidiously takes the aircraft closer to the edge of the flight envelope.
Although the system obviously works most of the time, there is a weakness if the system uses 3 identical tubes to detect a problem. If the problem effects all 3 equally, then it can be missed. It will be unreliable, but not recognised as unreliable. Just as three 2nd graders can't together do 6th grade math, 3 problem tubes can't reliably determine airspeed (nor even the state of unreliable airspeed).
With pitot tubes, you are using air flow through the tube to create a pressure, which you then compensate for altitude by using static sensors, and then converting this compensated pressure back into flow (or airspeed). There are a lot of links in this chain. Even worse, a problem could generate either an over-speed (eg blocked pitot drain hole) or an under-speed (blocked tube).
When it is difficult to measure something important, an alternative that is easy to measure becomes important. And so it was 200-300 years ago - flow was difficult to measure, pressure was easy, and so we calculated flow from pressure.
Maybe the time has come for us to measure flow, and thus airspeed directly. Presumably that is the principle behind the laser systems currently being developed.
It may be that pitot tubes today are dinosaurs looking for a tar pit.