I always shot with primes during most of my photo career. Earlier zoom lenses for still cameras were so poor that few self respecting photographers would use one. When I shot with my first zoom lens (a 43-86mm Nikkor during the mid 1960's) I absolutely loved shooting with it because it seemed so versatile. That is I loved shooting with it until I saw the images it produced and then, I never picked up the lens again (I was a Navy photographer and had access to a large variety of lenses).
However, by the time the EOS cameras and lenses came around the quality of the zooms had increased dramatically.
Yes, prime lenses usually are still faster than today's zooms. If you absolutely need a fast f/stop for venues like indoor volleyball or basketball without flash, the primes are the way to go.
Yes, individual primes can be less expensive than zooms but, it is often as expensive to purchase several primes to cover the focal length of a zoom AND, I personally do not like shooting with primes unless I shoot with at least two cameras. Otherwise, I will be missing a lot of shots while changing lenses.
Yes, the image quality from some selected primes might be a bit better than from selected zooms. However, top line zoom lenses provide sufficient image quality for all but the most dedicated pixel peekers. However, we are considering use of the entire frame (whether that be a full frame, 1.3x, 1.5x or 1.6x crop). I am most often able to utilize the entire frame when I am shooting with a zoom lens because I can crop in the camera. When shooting with a prime lens I have three choices: be in the perfect spot for the photo, zoom with my feet or accept that I will need to crop at least some of the image. Choices numbers one and two are not always available and choice number three will degrade the image somewhat.
IMO a top-grade mid-range zoom lens with a constant f/2.8 aperture should be the anchor of every serious photographer's lens battery.