Strictly speaking, image stabilization (IS) is not a necessary feature for any lens. For the vast majority of the history of photography IS as we refer to it did not exist. Plenty of remarkable photos were taken in spite of the lack of IS. The ultimate method for camera/lens stabilization will always be a stable tripod with a quality head attached and a way of releasing the shutter without directly touching the camera.
It is true that the benefits of image stabilization are most obvious when using lenses with a very narrow angle of view. The same amount of camera movement when using a 300mm lens will blur by a factor of 10 the number of pixels as when using a 30mm lens. But that does not mean there are no benefits of using image stabilization on a wider angle lens. Whether that benefit is worth it to you depends a lot on what kind of conditions you find yourself in when shooting. If you must shoot handheld in low light and your subjects aren't moving very fast, IS can make a real difference.
For most of the time I have been using SLRs I was of the opinion that any lens with a focal length of 50mm or less didn't need IS. My experiences with the EF 24-105mm f/4 L IS and the EF 17-40mm f/4 L lenses have modified that position somewhat. I can get away with slower shutter speeds with the stabilized 24-105 than I can with the non-stabilized 17-40 when shooting in the focal lengths they share. Regardless of how good your handheld technique is, you can stretch that good technique even further using a lens with good IS if your subject is stationary.
I'm still not willing to sacrifice any significant optical quality for IS in the shorter focal length lenses, but I am willing to pay a little more for the times when I can benefit from IS in a wider angle lens that allows me to shoot at very slow shutter speeds when photographing still subjects in low light. In the film era (and my younger days) I could shoot handheld at 1/15-1/30th second with a 50mm lens and get about a 50% keeper rate. I'm a little older and less steady now than then, yet I can still shoot at around 1/5-1/10th second with the 24-105 set at around 50mm and get better than 50% useable shots!