I almost sold all zooms as they had only 1 advantage : zooming, and all was said..
My types of photography are :
1.Urban exploring (shots of abandoned rooms inside) :
In past I used the best optical zoomlens possible : the Tokina 16-28 2.8 zoom
It's the only lens I used for this type of photography, but honestly I used it always at 16mm, the zoomrange to 28mm wasn't that big or interesting.
Although my tripod is the most stable, my camera fell on the ground and a part of the lens hood cracked, it was heavy as a brick! The only optical negative was the flare (bold lens).
I replaced it with a Tokina 17 3.5 ATX Pro prime, out of production (thanks Ebay)
Man, a world of difference, superlight, no flare, compact and equally sharp, a joy to use it.
Advantages of primes :
-Faster focusing in lowlight (less hunting)
-More atmospheric pics in lowlight without flash
-Lower iso's in lowlight so less noise
-Primes are sharper (less glass)
-Dreamy f1.2-f2 bokeh
-More compact and lighter
Disadvantages of primes :
-You need more primes to cover the distance so more expensive, but after a while you know which mm's you need.
-Some have CA, but if you chose the right primes you can minimize this
-No zooming capability
But for me I find it boring to have for example a 24-70 or 24-105, I had 3 of them in past.
It's just like you have a compactcamera, start zooming lazy in your seat and have no bokehlicious wowpictures, being able to isolate a subject with a sweet bokeh is a great advantage for portraits.
The only magical zoom I kept is the 70-200 2.8L II, ideal for events & modelphotography and wowpictures with nice bokeh thanks to the combination of 135-200mm focal length + f2.8.
Maybe i'm too picky, but even on holiday I use my 35 1.4 Art + 70-200 2.8LII.
So they are complimentary, but for my experience (bought/sold many lenses, yes i'm a gearhead ), I ended up with primes as they are more pure optics.