Ideally, the ETS would administer an IQ test and call it the GRE, but because we can’t have nice things, we have to settle for testing something that is close to intelligence. However, that doesn’t mean that the GRE (aka the crystalized intelligence test) cannot be improved upon.
Nice suggestions. I definitely think using computerized adaptive testing to a greater extent would help squeeze more g-loading out of fewer questions.
Adding speed rounds is maybe a good idea, but I can see there be complications with practice effects. In my experience, it's easier to practice thinking faster than it to think deeper. So adding speed rounds, would encourage people to practice for the test more than its current format (which encourages memorizing vocabulary, but is otherwise hard to practice for).
Practice is not bad in and of itself: you can have a standardized test where the expectation is that population has practiced beforehand (that's how the LSAT and MCAT works). But the GRE is meant to be a quick-and-dirty standardized test, not something to be grinded for.