Monopods are smaller, lighter, and more portable than tripods. As a result they're easier to carry around all day when out shooting. Many monopods fold down very small and can be stowed in a large pocket. Carbon Fiber monopods are typically exceedingly lightweight.
So, a monopod has a major advantage over tripods in portability, but that's not the only advantage.
The other major advantage of monopods over tripods is setup. If your monopod is preattached to your camera/lens, getting ready for the next shot requires only that the foot of the monopod needs to be put on the ground. On the other hand, when using a tripod, at the very least you need to splay the legs, set down the tripod on the ground, and likely loosen the head to be able to position the camera/lens to focus on the subject. All that takes more time than getting a camera/lens on a monopod ready to shoot. Often you'll see photographers carrying around their camera/lens on tripods with the tripod legs presplayed, in order to reduce the time needed to be ready to shoot.
When using a tripod for wildlife shooting, I've definitely occasionally missed a photo or two because of setup time.
Wildlife and sports photographers often prefer monopods over tripods because of their fast setup time, and their ability to allow the photographer to quickly move the rig from position to position to move from subject to subject. While the stability gained by using a tripod is in excess of a monopod, there is no doubt monopods significantly help photographers keep their camera/lens stable much more than only by hand holding, especially when using long/heavy lenses, when good monopod technique is used.
When using "long" lenses (~ longer than 400mm) it is hard to hand hold a shot and keep it steady enough to avoid camera shake to get a sharp image. Moreover, to do the same repeatedly over a day, gets harder and harder as you get more and more tired from picking up and holding the lens. Using a monopod can overcome this.
I think that some might also tell you that monopods outperform tripods when shooting moving objects such as birds in flight or race cars going around a track on in a road race. They would suggest that the freedom and ease of movement which the use of monopods have, exceeds that of tripods. In this area I disagree. Freedom and ease of movement of tripods is largely a function of the tripod's head. If you utilize a gimbal mount on a tripod, one can move the camera/lens to follow birds, race cars and other moving objects extremely easily, and once setup, from a "platform" more stable than a monopod.
That being said, if you go to any football (American or soccer) stadium, for example, the pro photographers are using monopods, not tripods. That's because of the speed of setup, and the need to move position quickly, plus in this case, the amount of room each photographer has for shooting.
In the final analysis, monopods aren't "emergency or last solutions" when tripods aren't accessible. Monopods are chosen proactively by photographers for the advantages they bring them under specific shooting circumstances.