The first rifles that came out tended to be tubular magazine. Then they noticed with military ammo (longer cartridges than the winchester 1879, for example), you could fit more ammo in a box than in a tube (10 rounds in the SMLE, for example) and it was a lot quicker and easier for reloading. With bullets becoming pointed (spitzer bullet adopted by the german army in the 1890's) and hard (copper jacket instead of lead), in a tubular magazine one bullet's pointy tip sticking into the percussion cap of the next one (and so on up the tubular mag) and with the dodgy percussion caps of the 1890's, accidents will happen, so box magazines were just safer.
You don't have to worry about shotgun ammo having a pointy tip and setting off the next cartridge above it and the box magazine evolved from the tubular magazine so shot guns just stayed the same, it was rifles that changed.
Also shotguns were never really viewed as combat weapons until recent decades and were primarily used for sporting purposes before that. As you don't really need to worry about the turkey/rabbit/pidgeon/pheasant you just missed getting his gun reloaded before you, having a slow loading tubular magazine didn't really matter.
As to bolt action being prefered on non automatic rifles to lever action or pump, that's because the bolt/reciever lock when the bolt is fully closed on a bolt action, especially if it has forward locking lugs (mauser/ remington 700) instead of rear locking lugs (SMLE), is much more solid than on a lever or pump action (or straight pull bolt action, too), and as a consequence it is much more accurate for a rifle to have a bolt action. In shot guns this doesn't really matter as they are by definition short range weapons that scatter the contents of their cartridges over a wide area of the target. If you're shooting slugs in a shot gun your using the wrong gun for the job unless you're shooting at very close ranges.
Also have you seen the size of shot gun ammo? Even a ten round box magazine for 12 gauge ammo is huge. Most assault shotguns can hold 6 - 8 rounds. If you haven't got him with those first six to eight rounds then you need a bigger target or he's probably got you already anyway. Unless you're out hunting, in which case if you missed him six to eight times the turkey DESERVES to get away.
That's just my opinion, hope it's some help.