Unfortunately, the whiteboard thing is not as standardized, so it's somewhat harder to teach to the test, but it is not impossible. People waste a lot of time I think when they can memorize a small number of basic algorithms and then learn to map the question given to one of those techniques.
But writing the code with a marker on a board definitely takes practice as well.
The available training materials are good, but they are not great. A focus on shortcuts would be nice. I remember my verbal SAT improving significantly just from the single tip to read the reading comprehension questions before reading the passage. I suspect there are similar tips that can improve your speed at figuring out the trick that solves these interview problems quickly.
So, I generally feel like it makes more sense to try to determine the actual aptitude when you have an opportunity, instead of trying to measure it by possible decades old proxy with huge and unknown variance. If you had good grade and/or spent some time studying for the interview, and really meet the hiring bar, you'll most likely do well in the interviews anyway. There's some noise in the process, and good qualified candidates are sometimes rejected, but from company's perspective, it's better to have some false negatives, than to give another metric that can be easily gamed, and get false positives. Google has enough qualified candidates applying for a job to make it not that big of a deal if you lose some due to the noise.