How useful is the GRE Exam? How useful is the GRE for the academic career/research/daily academic tasks?

It's not required in my country but I'm wondering about the intrinsic value of its study material.
The GRE's effectively only good for one thing - getting admitted to graduate school. You will need it if the program requires it as part of your application package. Most US graduate programs do require it. If you study elsewhere then there's a good chance you don't need the GRE.

About whether it's useful study material, note that the GRE is an exam, not study material. You can use the GRE as a benchmark to see whether you're mastering the study material, but not as the study material itself. As for whether it's useful, knowing more things is usually never worse than knowing fewer things. However, will knowing more about undergraduate-level e.g. physics or mathematics help you in your career/research/daily tasks? If you teach physics or mathematics, then presumably so (although at that point you probably don't need the GRE because you are already intimately familiar with the material), or maybe if you work in science communication, provide private tutoring, etc. In most careers though, it will be irrelevant, and you can ignore the GRE.