Why do I need a telescope for astrophotography?

Technically, you don't need a telescope for astrophotography, but for planetary work, it works a lot better.

For wide field, you're usually better off with a camera lens; a good prime will have better resolution than your sensor, approaching what even very slow films can manage. For high magnification, however, the reduced element count in a telescope (especially in a reflector, which also eliminates some aberrations that are very hard to remove from glass lenses) improves image quality.

Your zoom plus converter probably has sixteen to twenty elements total, each of which has surface errors, scatter, and reflections that degrade the image. A 100 mm f/12 refractor (what a photographer would call a 1200 mm lens) will have two or three elements in the form of a cemented achromat or apochromat.

Add to that the fact that many telescopes include some means of tracking the sky (nothing has yet beat a clock-driven equatorial mount, correctly aligned, for this) and for a camera, that's another add-on -- and you're probably ahead buying a decent telescope, with tracking mount, and a conversion to mount your camera on the focuser, compared to trying to get good images with a zoom.

A compromise would be to replace your zoom with a long prime -- 400mm aren't hard to come by, and play much nicer with teleconverters than zooms do. You'll still need a tracking mount, of course.

In principle, there's no difference between a camera lens and a refractor telescope.

While focal distance is related with the magnification of the image, in astronomy, resolution is related to aperture (not the F-ratio, but the area where light enters). So, if you increase your focal distance, without increasing your aperture, then you are not increasing resolution at all!

Every glass element also have some transmission loss. That is: reflected or absorbed light that does not reach the sensor. And for faint distant galaxies and deep sky objects, is very important to minimize transmission loss.

At last, remember that teleconverters not only increase your focal distance, they also increase your f-ratio. Since the lens/teleconverter device has more focal distance with the same aperture area.

In the end, a telescope has some serious advantages over a zoom lens with teleconverter:

1. No teleconverter means fewer elements and less transmission loss. Also, teleconverters may, and usually will, degrade image resolution and quality
2. Zoom lenses have way more elements than prime lenses and telescopes. More transmission loss and more image degradation.
3. Same quality and aperture tends to cost less, since you don't have unneeded features like autofocus and variable aperture.
4. If you use reflector telescopes, same apertures cost even less. And you may reach 10 or 12 inches of aperture.
5. Telescopes are compatible with astrophoto-dedicated cameras, and astrophoto-dedicated filter rings.

Of course, for wide field astrophotography, a camera lens is the best option. But I'd use a prime lens.

@vsis already said this, but I'm going to be more explicit:

It's all about the brightness. Most astronomical objects worth looking at are dim. The more light your optical system "gathers," the more objects will be available for you to see and photograph.

When amateur astronomers get together to talk about whose is bigger, the most important number you'll hear anybody mention is the aperture of their telescope. Other numbers, like the focal length of the mirror or, what they have in their bag of eyepieces are secondary concerns.