go install isn’t really an installer. Frankly I don’t really see the point of even having that option.
More broadly speaking, you shouldn’t really be relying on your compiler to do the install. That was never the intended behaviour of a compiler. Which is why history you’d find the install options in the build scripts (eg makefile).
I was referring to installing the Go compiler - as an arbitrary example of an application you want to be able to launch from CLI, but that doesn't set it up for you. (And instructs (Or did) you to use export.