There's an added benefit to having your feet shoulder width apart, and that is the ability to move quickly and fluidly. If you stand with your feet too wide, you'll have to bring them together in order to move; otherwise you'll be duck walking. The opposite is true if your feet are too close together; you'll have to spread them apart before moving. Plus, if your feet are too wide apart, or too close together, you can easily lose your balance, or be knocked off your feet in close quarters.
Whether too wide, or too close, both obviously waste valuable time because you have to switch your feet position before moving, and that's time you don't have in a gunfight. Although it may only take fractions of a second to move your feet, gunfights are won in fractions of a second.
The next part of your foundation is to bend your knees slightly. We don't walk or run with our knees locked like we're a bunch of penguins, so why lock them on the range during training? It's all about what comes naturally, or instinctively to you. If you were standing with your knees locked, how easily could you be knocked over? Bending your knees slightly, lowers your center of gravity.
The next step in your foundation is to bend slightly forward at the waist. Don't make the mistake some people do of dramatically leaning forward to try to counter the recoil; it will only make it worse. Just bend slightly forward at the waist like you do normally. Nobody walks, runs, or fights with a stiff back, so why train that way?
Having your feet shoulder width apart, bending your knees slightly, and bending slightly forward at the waist, allows your body to act as one big recoil spring. Your body is in fact absorbing the same amount of recoil from the shotgun as before, because that hasn't changed, but how you absorb that recoil is what makes the difference. If you doubt me, stand with your feet too far apart, or too close together, with your knees locked and your back stiff, and fire a round of buckshot from your shotgun. You'll quickly notice the difference.