Context is what defines what people use, without knowing in what context people use camera straps, you are having trouble justifying it. I can partially guess your typical context by your answer to your own question.
The strap I use is an extremely padded version of the standard neck-strap. It makes a world of difference for comfort but otherwise works the same way as the standard strap. Actually, it has a quick-release system which I rarely use.
- Faster lens changes: With the camera hanging right in front of me, it is in a great spot to change lenses which I sometimes do dozens of times per day. Going strapless it takes me at least twice the time.
- Fail-Safe: The neck-strap I use stays on my neck most of the time. If I setup my tripod on a precarious location, I keep my neck through the strap. Shooting downwards from a balcony, you bet a keep the strap on!
- Security: Makes the camera safe from accidental knocks. If it gets knocked or I get pushed, chances are the camera will not fall. In some environments such as crowded streets or markets, it is impossible to prevent something from knocking the camera. There is also no where to put it down.
- Hands-Free: There are plenty of things to do while taking pictures that work better with both hands free: handing out business cards, writing people's emails, handing model-releases, etc. Yes, I could store the camera but I'd need to back right away, specially if what I did was to get someone's photo!
- Anti-Theft: There are fewer chances someone can take away my camera if its attached to my neck. I also use the strap to look through objects while doing other activities. This is to prevent snatching not to leave it. I still watch it and have part of my body firmly against the strap, so that I can feel any movement. BONUS: Some camera straps have en embedded metal wire to prevent slashing.
- Multiple Cameras: The straps may get entangled but at least it makes it easy to shoot with multiple cameras.
- Noticeable: A camera strap makes it obvious that there is someone with a camera taking photos.
- Shooting Down: When shooting the nadir shot for a panorama, the strap needs to be carefully folded up to prevent it from showing up in images.
There are a few different straps which I use regularly, mostly with smaller cameras. My favorite for being stealthy is a Hand-Strap:
- More safety than no strap. Particularly from accidental knocks. Some are tethered to your wrist but mine is not (I know which I'll buy next time!).
- Tiring: With a handstrap you support the weight of the camera at all times, so I rarely use it with something big. There is also nowhere for me to put it except the bag while shooting with another camera.
There are tons of custom straps and I have an issue with all of them except for the Bosstrap:
- Block the tripod mount: Most rapid straps hook to the tripod mount which is annoying for using a tripod.
- Poor tripod contact: Even the few models with a pass-through offset the mount and your camera is no longer aligned on its optical axis. They also reduce the contact-surface between the camera and quick-release plate.
- Where is the bag?: Have you seen the videos selling rapid straps? People never use a camera bag! My guess is that it would get entangled with a shoulder-bag (my favorite) and not work at all with a sling (second favoirte) and probably cause difficulty with a backpack (never use one for photography).
There are more complex options aimed at professionals but which I have never used:
- Harness: Good comfort and distribution of weight. Holds multiple cameras easily. Extremely secure.
- Holdster: You can have holders which attach to your belt (actually, a friend had two sown to a padded belt) and simply draw the cameras out and drop them back when you need to free your hands. This worked well for 2 cameras with one lenses each but probably wont scale.
- Belt-Clips: At a local store I saw a clip that attaches to an ordinary belt with a matching piece that screws into the tripod-mount (not my thing) but lets the camera slip and lock into the clip quickly.