I find the Nolan Chart (https://www.theadvocates.org/political-type-comparison/) to be a better version of the 2D compass. You're absolutely right that more dimensions would be better, but finding the right orthogonal ones is difficult.
The Nolan Chart is superior to the simplistic left vs right of U.S. political discourse in part because it shows there is more variation than the major parties would like everyone to think.