Imagine making the GRE a three-hour test instead of a four-hour one. All you have to do is skip both AWA essays. And if you already taken the GRE and have scored really well on both essays what is there to lose, right?
The answer is an awful lot, depending on the programs you are applying to. For the most part, skipping the AWA essays may be disastrous. Below are a few points to keep in mind if you are thinking of skipping the AWA portion of the GRE.

Undercuts your competitiveness

For a moment, imagine your job is to look over applicants. You have a strong program, which you are proud of, and therefore you want only the best candidates.
You have come down to the final slot and are deciding between two candidates. Both have excellent academic credentials and strong letters of recommendations.
One student has a 336 GRE score, and the other has a 326. The student with the 336 also has another interesting number next to his score: a big fat 0. Well, actually two big fat zeroes, since the AWA Essay score will read as such: 0.0.
The other student, by contrast, has a 6.0. Whom would you select?
The answer is not black and white. Perhaps, the program does not care much about essays, and is focused more on the quant score (in this case GRE 336 wins out).
Nonetheless, there is something about those two zeroes, a certain whiff of…fecklessness. Or is it smugness? Whatever GRE adjective I decide to employ, it is not a positive one. And because I, as an admissions officer, care deeply about my program, I don’t want to let some slacker in. Now, a suddenly highly propitious candidate has become passed over.

Does skipping really help?

Saving your mental juices for the actual test may seem like a reasonable basis for skipping. But will you actually do better on the test by diving into the multiple-choice part right away?
For one, the AWA section can actually help warm up those mental juices. Perfunctorily filling out some personal information only to be suddenly thrown into the GRE tempest can actually be harrowing. Once your “writing” and “critical thinking” brain have come alive in the essay sections, you are ready to begin the multiple-choice sections.
If test fatigue is an issue, remember there are better ways to combat it, instead of skipping the AWA section. For one, you can prep by taking more practice tests at home.

Is my program writing-centric?

If the answer to this question is yes, then the last thing you want to do is skip the AWA. Even if you are not entering a Creative Writing program, many programs—from Economics to the Biological Sciences—still place a strong emphasis on writing. After all, in grad school you will be writing your own papers.
As an admissions consultant, I would not only be very wary of a 0.0 student. I know that student clearly can write an essay that does better than an 0.0 (short of writing in Swahili, even a few choppy sentences will give you better than a 0.0). Nonetheless, I really won’t know what this student is capable of in a writing context.

Is it a retake?

Some would argue that if you have already score a 6.0 on your first take and only are retaking the test to up your general score, then skipping the AWA is a no brainer. But this isn’t necessarily the case. Again, there isn’t any connection between skipping the AWA and getting a better score.
Also, it is hard to really difficult to discern the impression your 0.0 will have on the person evaluating your report. And with so much at stake, are you really going gamble on such a thing?