It's that simple, right? Try to tell that to one of my readers who had a mole removed at the base of his penis and lost his ability to have an erection! The doctor did not realize, apparently, that there are key nerves that run down the side of the penis (that faces outward). Mole removal can go quite deep and this was utter foolishness on the doctor's part.
This story illustrates why the above equation is a gross simplification that ignores one of the most important parts of an erection: the nervous system. Erections are much more than just the sum of your arteries and hormones, which is one of the reasons that Psychogenic (Psychological) Erectile Dysfunction can play such a big role for some men.
Furthermore, nerve-related issues are one of the most
Researchers first noticed the criticiality of healthy nerves in an erection through studies of diabetics. Peripheral europathy refers to any malfunction or damage to nerves throughout your body (as opposed to your brain). Several studies in the 90's documented what physicians already knew: diabetics frequently have significant significant nerve dysfunction that leads to symptoms such as decreased feeling in the limbs, numbness, tingling and so on. Obviously, considering that the penis is a sort of limb, researchers were not too surprised to find that erectile dysfunction was much more common in those diabetics with peripheral neuropathy. 
Since then, a number of nerve-related issues and neuropathies have been found to be a significant contributor to erectile dysfunction. Here are just a few examples:
1. Bicycle Seats. Most standard bicycle seats will temporarily or even permanently injure the all-important pudendal nerve that carries the signals to initiate and maintain erections. This has a been documented in a number of studies, but one the most well-known was one that showed a no-nose seat significantly protected bicycle officers who rode many hours throughout the week as part of their job.
2. Non-diabetic Neuropathy. One 2002 study looked at patients with and without erectile dysfunction and they controlled for diabetes, high blood pressure and age. What they found was that neuropathy was independently correlated with erectile dysfunction, regardless of age, hypertension or diabetes.  The bottom line is that protecting your nervous system is every bit as important to your sex life as protecting your arteries. And, furthermore, you cannot blame "getting old" in this case either.
3. Spinal Injuries. Spinal injuries can also impair or damage the sacral plexus nerves that transmit erectile signals to the penis. Some of the most severe erectile dysfunction is associated with these types of injuries. However, one should not assume that all hope is lost if you have a spinal injury: several studies have shown that Viagra significantly improves erectile function in these cases.  This likely means that some of the other standard supplements and foods will likely help in most cases as well.
NOTE: See my link on Neuropathy Remedies for more information on natural aids and cures for this condition.
1) The Journal of Urology , 1994, 151(4):884-9, "Erectile dysfunction in diabetic men: the neurological factor revisited"
2) Diabetic Medicine, Aug 1996, 13(8):700-708, "The Aetiology and Management of Erectile, Ejaculatory, and Fertility Problems in Men with Diabetes Mellitus"
3) J Sex Med,2008 Aug;5(8):1932-40
4) International Journal of Impotence Research, 2002, 14:433 439, "The neuropathy of erectile dysfunction"
5) Neurology, Dec 1 1998, 51(6):1629-1633, "Efficacy and safety of oral sildenafil (Viagra) in men with erectile dysfunction caused by spinal cord"
6) Ann Neurol 1999;46:15 21, "Randomized trial of sildenafil for the treatment of erectile dysfunction in spinal cord injury"