To your specific question: "I'm not sure why assault rifles are necessary, etc."
Let's examine that, because your uncertainty reflects a combination of operational naivete' and some subscription to agenda-driven hyperbole.
First, the term "assault rifle" was invented by the Germans in WWII...the Sturmgewehr 44 combines the rapid fire of a machine gun or submachine gun in an infantry rifle size and cartridge.
https://en.wikipedia.org/wiki/StG_44
But it's a fully automatic weapon. A military weapon. It's functionally quite different than what the public can now own...though most of the public thinks that the AR-15 is the same...
The term was resurrected in the 1980s by gun-control advocates, who wanted to vilify semi-automatic rifles that were patterned after, but functionally different than, the Sturmgewehr or the AK-47, or the M-16. It's a term meant to sensationalize, to fan the flames of emotion....and it works, because the press keeps repeating it, without understanding the details of what is being discussed. It works to the point that Diane Feinstein's proposed "Assault Rifle" ban legislation defines an "Assault rifle" in a way that includes many target rifles, old hunting rifles, and rifles that really are just for sport.
Semi-automatic rifles fire one round for each trigger squeeze...this is the same operation as many shotguns, pistols, etc. This kind of operating mechanism has been around for about 100 years. The Colt 1911 is over a hundred years old, and it's a semi-automatic handgun.
You'll note, I hope, that the National Firearms Act of 1934 (NFA), made the required NFA firearms to be registered and taxed. NFA weapons were machine guns, short-barreled rifles (SBR), short-barreled shotguns (SBS), any other weapons (AOW or concealable weapons other than pistols or revolvers) which includes grenades and destructive devices, and silencers for any type of weapon. The $200 tax was quite prohibitive at the time (equivalent to $3,526 in 2015).
The act was amended in 1968, and gun control law passed in 1986, know as the "Firearm Owners Protection Act" (FOPA). Prohibited the sale to civilians of automatic firearms manufactured after the date of the law's passage as well as required ATF approval of transfers of automatic firearms...ironically, it didn't really protect firearm owners...it banned a certain class of firearms forever...but such is legislation, speciously named for a world interested only in sound-bite level understanding of the issues...
So, where are we now?
There lots of semi-automatic centerfire rifles on the market. They're the modern (last 100 years) standard. The M-16 design is over 50 years old now. It's dated technology, but it's the standard. They're used for hunting, target shooting, and yes, self-defense. This is a hunting rifle from Remington:
http://www.remington.com/product-families/firearms/centerfire-families/autoloading-model-r-25.aspx
It meets the definition of "Assault rifle", but it was designed for the reasonable purpose of hunting. Light weight, semi-automatic, magazine fed. Good handling, modest recoil (from its gas-operation). It represents what a modern rifle should be.
The M-16 architecture was introduced to the public as the Colt AR-15 about 40 years ago. A semi-automatic rifle with a detachable magazine. It's black...and in profile, looks like the M-16/M-4 family of weapons...but it operates differently. It's a semi-automatic. About 30 million have been sold in the U.S. - including rifles like that Remington above.
When my youngest learned to shoot at the age of 13, she got specialized training at a Navy small arms range, under the supervision of a SAMI, on a simulated M-16 that used a laser to score hits. Great opportunity by the way, and a great way to learn; instant feedback, no recoil, no noise, patient debriefing by the SAMI on weapon safety, operation, proper trigger control, etc.
She then moved on to the real thing. My Armalite carbine. A 16" (which makes it NFA-compliant) rifle with iron sights, similar to this one:
https://armalite.com/shop/m-15-carbine/
Why would I choose that rifle for a young shooter? Light weight and low recoil make it easy to shoot. The shorter barrel, and adjustable stock, which people want to use to classify "Assault rifle", make it possible to customize the fit to her smaller stature...and then customize so that her older brother, sister, and Dad can shoot it.
It's ideal as a sporting rifle. Light, accurate, simple, adjustable for shooter stature. That's a large part of why it's so popular: it just plain works.
Now, ironically, the 5.56mm cartridge that it shoots (or the .223 Remington that it can shoot) are considered too small for humane deer hunting in many jurisdictions...so, I laugh at the displayed ignorance when people describe the rifle as "high-powered"...well, no...it really isn't...it's designed to be light weight...and it uses modest ammo to meet that goal. I am astonished when people (Mr. Vice President) say, "You can't control that"...well, unless you're a 13 year old girl, in which case, you can punch bullseyes quite well with it.
Those handling qualities make it suitable for defense as well. It's not my first choice, I prefer my H&K pistol, through which I've put over 10,000 rounds, but for many folks who don't have the hand strength to handle a pistol, a carbine (a shorter rifle) is a good choice. Police in lots of jurisdictions have a similar carbine in their cruiser because handguns simply don't work at range. The cops that took down the Oregon shooter were ALL equipped with M-4 style carbines and Holographic sights as they entered the building. If it works well for them in an offensive situation, then it will work well in a defensive situation.
So, why do I "need" so many rounds? Well, look at actual shooting encounters. If you look at police shootings, it turns out that many police encounters take multiple rounds to bring down an adversary. This isn't Hollywood, where Bruce Willis takes out each bad guy with one 9mm round, it's the real world, where training, adrenal response, moving targets, etc. all come into play. So, if the police hit the bad guy an average of 13% of the time (NYPD), and it takes multiple hits to stop him, then to get two rounds on target will take about 15 rounds in your magazine...so, if you're facing two bad guys, looks like 30 rounds is about right...
These are real shootings by the way, where the cops are facing an armed, active threat. Mass murder is a different topic...if you line up people and shoot them at close range, you clearly don't have the challenges that a cop faces. So, in real world defense, 30 rounds in a carbine would be a minimum...and for my H&K, I have 12+1 in the pistol, with two spare magazines of 12 each...
This is why magazine capacity limits are such a poor idea. They restrict the effectiveness of the weapon in its legitimate use: self-defense. It's beyond infringement...it's denial of the effective weapon.
The state of the art changed to magazine-fed semi-automatic over 100 years ago. We can't get that genie back in the bottle, despite the rhetoric. And to be fair to the folks that want to exercise their right to self-defense, we shouldn't try. They should be allowed to use the state of the art from 100 years ago, like the Colt 1911, or even 50 years ago, like the AR-15.
