The bolt rifle and semi auto have risen to the top of the popularity heap for a reason. Pumps have languished for a reason as have the "modern" lever actions such as the Savage 99, Browning BLR, Winchester 88, and others. The traditional cowboy levers are somewhat popular for nostalgic reasons, not practical ones.
Bolt rifles are by far the lightest, have the greatest accuracy potential, are the simplest designs, can be built for less money, and will handle hotter loads that will choke a pump, lever or semi. If someone practices rapid fire drills they are amazingly fast enough for aimed repeat shots. You can unload a magazine through the bore a little faster with a pump or lever, but if the requirement is to actually hit a target with the rounds a bolt action will hang with either.
Semi's give you speed and wins the hit em fast contest by a wide margin. They can be accurate enough.
Pumps and especially levers are fascinating, but complex pieces of machinery. I love my levers, but from a practical perspective they offer no advantages. Not as fast as a semi, generally not as accurate, cheap or light as a bolt gun. While they theoretically should be a tiny bit faster for repeat shots that is only offhand. If firing from any type of supported position, a tree limb, with shooting sticks, bi-pods, or prone both are essentially single shots.
Both designs were tested by the military in the early 1900's and proved less reliable and too slow to operate and reload compared to bolt rifles.