Of course if you have a zoom lens that covers the focal length of the prime, the two will be essentially similar if you don't zoom it. But I think one advantage of a prime is that it prevents recomposition by zooming. We could go on and on with an argument about the pedagogical importance of prime lenses, manual exposure, and so on, and there are practical limits in the real world on how far you can "zoom with your feet," but if you must recompose by moving around, then you will move around, and in the process may see things differently, while preserving the perspective you started with.
In addition, I think that if you use a "normal" perspective lens, and get the composition right, the subject will be what people see the most, without the distraction of unusual perspective or equipment.
It also doesn't hurt that most good prime lenses will be well behaved, with less aberration and flare, than their equivalent zooms. If your intended quarry is in the range of a prime, a zoom may be an unnecessary encumbrance.
I still travel with zooms for the fairly obvious reason that I can't step off a cliff or jump into the ocean to change my framing. And at other times I like odd and exotic focal lengths for the very reason that the image I want to make is not "a picture of a thing." But for many other things, I find I prefer a normal prime (35 in my case, since I'm using DX), because it "sees" what I see. There's a simplicity here, that what you see is what you get. Of course you can make all sorts of abstraction still, but when you want the subject of the picture to be what it's about, this is, I think, the best route.