Good post from Old Smokey. Just my two cents to follow.
There is ongoing research on new ways to measure airspeed using lasers BUT such systems would measure True Air Speed (TAS). Of course, TAS like GS are important data for navigation but a pilot would still need CAS or its close cousin EAS. This is because aerodynamic forces acting on an airplane are directly proportional to dynamic pressure hence CAS helps a pilot flying safely and accurately an airplane. BTW, all operational limitation and performance data that depend on airspeed are better and more simply expressed using CAS than TAS. Automatic systems also need to use CAS.
Now, to get CAS or EAS from TAS you will need temperature, static pressure and a few lines of code in a computer. This means that you need one more probe than with pitots: a TAT probe which is itself as prone to icing as the Pitot tube. Incidentally, it is not clear yet that a laser sensor would be insensitive to icing.
In the end, it’s seems hard to build a more reliable air data system without pitots.
DJ