There are a lot of reasons. Pump shotguns are very durable and will continue to function after abuse that most other shotguns couldn't take. In theory a pump shotgun is more reliable, but in practice semi-autos are. Most pumps fail because of operator error but if kept reasonably clean a semi-auto will be more reliable. That's not the same as rugged. Pumps are more rugged and handle abuse better. In a TEOTWAWKI situation I want a pump. But a semi-auto is in my closet near the bed.
Pump rifles much less so because of the much higher pressures they work at. Low powered rounds like 22 and some of the pistol cartridges do OK, but pump and lever action rifles are the least reliable, least rugged rifle actions, especially if used in harsh weather.
Fast follow up shots are overrated. Emptying the magazine fast and hitting the target fast are 2 different things. I've timed myself firing 3 shots as fast as possible, but just throwing lead downrange with no target. I got of 3 shots from a bolt action 308 in just under 2 seconds. A pump was about 1 1/2 second and a lever action 30-30 about 1 3/4 second. A semi-auto was just under 1 second.
But when I placed a paper plate at 50 yards with the requirement that all 3 shots MUST hit the target my times with the bolt action, pump, and lever action were almost exactly 4 seconds. The semi-auto was closer to 2 seconds.
Old school bolt rifles tended to be heavier than lever actions, but that is no longer true. I have several bolt guns that weigh less with scopes on them than my Marlin 30-30 weighs with no scope. Some a lot less, as in under 6 llbs scoped compared to 7 1/4 lbs for the Marlin or about 6 1/2 for a Winchester 94. And with shorter overall lengths.
When fired from any type of supported position pumps and levers are SLOWER to get off repeat shots than bolt rifles. If you want to use your pack as a rest, use shooting sticks, or even a tree branch for support a bolt gun is faster for repeat shots
That's part of the reason neither were ever seriously considered by the military. Neither is very rugged and are easily taken out of action in mud, snow and ice plus they can't be used prone. You can't lie on the ground and shoot out of a fox hole with them. You have to raise up and be exposed to return fire to cycle the action.