One of the most puzzling mysteries of modern day Physics is why mathematics is such a useful tool for uncovering the workings of the universe. Although mathematics has always been the only acceptable language in which to phrase serious physics, letting mathematics guide the direction of physics is a late 20th/21st century revolution in scientific thinking.
We can get most of the way to deriving the constancy of the speed of light just from the Principle of Relativity alone. In other words, the speed of light being constant is just a consequence of the laws of physics being the same in all inertial frames.
While I will be quick to point out that a theory of quantum mechanics based on consciousness has not been ruled out, it is certainly not the only way to formulate the laws "in a fully consistent way". Pilot wave theory, GRW collapse theory, many-worlds theory, and decoherence theory are all consistent attempts at trying to make sense of quantum mechanics.
Embracing wave-particle duality helps us to come to terms with the strange results of the double-slit experiment, but it leaves us with a very confusing picture of what an electron actually is.