Lenses are all best when stopped down a little. An f1.4 lens will be better at 2.0 than 1.4, and perhaps better at f2.8 than 2.0; it may be "best" at f2.8. Similarly, an f1.8 lens will be better at f2.8 than 1.8; it may be best at f4. So, if I expect to shoot at f1.8-f2, I would likely be better served by an f1.4 lens than an f1.8 lens.
At any aperture I use, the depth of field is controlled by two things: the aperture and subject distance. So if I want to take a photo at f1.4, lets say of a person, and they are close to me I may have trouble keeping focus on both eyes because of how shallow the DOF is. But if I back up and refocus, that same f1.4 aperture will be able to keep focus in both eyes, out to the nose and back to the ear. Increasing subject distance increased depth of field at the same aperture.
So, it's entirely possible to do street photography and have focus on both eyes at f1.4, so long as the subject distance is adequate. (In fact, I have a friend whose street photography is shot almost exclusively at f1.8.) Food photography -- where the distance to the subject is very small -- emphasizes the thin DOF that shooting at f1.4 offers.
At any rate, I can think of two clear scenarios where shooting at f1.4 might be preferable:
- Creativity. Being able to show a thin slice of something places specific and definite emphasis on that specific subject.
- Darkness. Shooting with a high ISO and large aperture will allow you to capture a moment you may be completely unable to capture at f4, for example, and have a photo with thin DOF is better than having nothing but a blurry frame.