Why isn't Nyquist taught like this?
There is no problem with the method you propose.  It's the one I've used for years designing real systems.
You were probably taught a graphical method (I'm curious as to what it is -- do you have a link?).  The graphical methods were invented before digital computers, or even calculators, were ubiquitous, and were designed to make it easy for an engineer with pencil, paper, a ruler, and a slide rule to make the graphs needed to get the job done.