Zoom lenses are great. I mean, they are really wonderful, amazing things, which will help you achieve all sorts of things with your photography. Zoom lenses give you so much more versatility than prime lenses, and in situations where you're unsure what circumstances you'll be taking your photos they are vital. Zoom lenses also give you effects unachievable in a prime lens, such as compressing the fore- and backgrounds. In short, you should have an array of zoom lenses in your photography arsenal.
However, zoom lenses are also a problem, especially for beginner photographers. They can be a problem because they can make you lazy.
In pretty much every photography course you might be likely to take, "Get Closer" will usually be the subject of one of the first lessons. This isn't by happy chance. Using a zoom lens to magnify your subject is all fair and well, but you will lose definition, struggle to get your focus correct, and, if you're not on a tripod, keep the camera steady (which is always harder with a long, heavy lens hanging off the front of your camera).
Getting physically closer to your subjects will help you in a range of ways. Correct focus is likely to be easier to achieve, and your definition will improve, especially if you are using a prime lens (which simply provides better image quality). Being able to get your focus correct is going to mean you'll be able to open up your aperture very wide and achieve a beautiful shallow depth of field and more interesting bokeh (that is, the ascetic blur in your out of focus areas). Getting closer to your subject is likely to improve your image immensely, and will help to achieve both better image quality and more intimacy with your subject.
So go out and try it!
Here's an example I took back in October of my good friend Bailey The Golden Retriever. It was taken on my Sony a7s using a Zeiss 35mm Prime lens, shot at 2.8f to give me enough depth of field to get both his eyes and snout in focus, but causing nice bokeh on the interesting background of the Eaton Park rotunda in Norwich.