I can see the utility of this from the point of view of trigonometry. At one point in the chapter he gives an example of a simple problem that is needlessly complex to do using tan (if you dont have a calculator.) As such a knowledge of this would surely be useful.
However it is not clear to me how you could use spread to map a continuiously increasing quantity (such as time) on to a periodic variable (such as displacement.) Surely to do this using his simple ratio of quadrances would be more complex than using sin? Then what about things like Fourier series? This would surely be very clunky in this framework.
This stuff must still be equivalent to classical trig. Thus it cant possibly be 'revolutionary'. You still need to start with the same axioms.