Additionally, you aren't intended (for many situations) to use a single "main" Zephyr install, but to include what external modules you need in your project's west.yml. If you have a number of projects sharing the same Zephyr install that's a separate discussion but installing every possible toolchain/HAL is not the only way to do things.
Also it should be trivial to build using the GNU Arm Embedded toolchain if the author did not want to install the Zephyr SDK, not sure why this did not work for them.