To replace an effective technology, propose a better technology for that particular application.
The Stewart platform (as shown) would add both weight and complexity, and therefore cost and potential performance limitations, to a function already accomplished with less weight and less complexity. As @Therac pointed out, tilting the rotor is not necessarily impossible, but this mechanism would not replace the swashplate.
Direct motors or servo flaps can do that, at the cost of requiring
constantly correcting computer control.
This means that you have to build yet another subsystem to do that: adds weight, adds cost, adds complexity. Granted, complexity itself is not an "all stop" design consideration (or helicopters would not be flying today :) )
Let's consider the next issue: consequences of failure. If you put this system into place, what happens when it fails/breaks? What does the rotor system do, or not do, as a consequence of that? How are the loads being transmitted through the airframe/flight control system in this case?
The Stewart platform is fit for purpose for a variety of applications (one being motion in a flight simulator) but when it comes to helicopter design, you have to earn your way on to the aircraft in terms of the weight required. Until you can explain how this system is better than the system that has been shown to work, what incentive is there to apply that? Given its proposed relationship to the flight controls, which are critical to both function and flight safety, there isn't an incentive readily apparent.