A lot of it has to do with some actions or types of rifles are just "what you get" when you want to fill a niche with any given properties (e.g., SHTF, hunting, etc.). After a few decades (or generations) of such an attitude, certain guns get refined for certain tasks. Can a pump rifle be as durable as a bolt rifle? Maybe. There aren't a lot of people who express problems with the millions of Remington 870s out there, and they're generally much higher volume shooters than .30+ caliber rifles (over the life of the rifle/shotgun anyway). Can it be as accurate? (Not to be confused with "can it be accurate enough for a given prupose?") Well, in this case, unless it has a free-floated barrel, it probably won't be capable of sub .50" groups at 100 yards. That's a question that gets asked pretty often when, in fact, maybe the quesiton that should be asked (pragmatically) is "does it have enough accuracy to hit the COM/kill-zone out past 600 yards?" It is a source of some amusement to me when people poo-poo a rifle as inaccurate when they are, ah, possessed of limited field marksmanship themselves. The difference between .5" @ 100y and 1" @ 100y is largely negligable when shooting in field positions. (By "largely negligable," I mean "completely negligable" to most shooters (like myself). I don't know too many shooters than can shoot sub-MOA groups off hand (or in one of the more traditional field positions such as rice-paddy prone) with a rifle they'd be willing to take to the field. And by "too many" I mean "any" (that I'm aware of anyway)).
While there are some mechanical issues (best possible accuracy), the issue holding most rifles back from filling what we'd consider "untraditional" roles is usually us. Remington brings out a pump rifle, but most people are used to using levers for short range hunting and bolts for longer range work. Nobody quite knows how to receive this new (more or less) object that resists classifiction until Uncle Jim Bob bubba's his 7600 and, by word of mouth, everyone becomes aware of one (or more) inherant flaws in the weapon's design. Some people take to it because it fits them properly, but by and large people recite gunshop stories from people they've only heard of about a weapon they've never fired and it fades into nothing more than a curiosity.
Ah, the sordid tale of the 7600, at least it serves as an example.
As for the more specific question of what keeps bolt actions from being considered defense guns, well, have you tried to find a .223 or .308 with an 18" barrel and *good* iron sights lately? Yeesh. It's almost impossible. There are one or two out there, but most are longer barrel guns with no irons. By contrast, most levers/autos *are* short-barreled and iron-sighted. Provided you could find a turnbolt that has a reasonably short OAL and can take a good set of irons, I don't think you'd be terribly underarmed. Most only hold four or five rounds, but that's a whole other argument altogether.
FWIW, I think Remington makes a "police" version of their 7600 which has a slide release and safety located in the same position as the 870, takes a detachable mag (AR-15?) and has the aforementioned irons and shorter length barrel. If you're interested in a pump defense rifle, this unit might bear further examination.
Edited to add: What Kaylee said. I'm not sure how "defensive" a 600-yard rifle is? Given the general state of rifle marksmen nowadays, though, I wouldn't be too terribly worried about it.