To start off, I love machine guns, and fully-automatic assault rifles. I train with them day in/day out as part of my job, and this is my opinion based off my limited experience.
We use our automatic selection and machine guns for suppressive fire, not for attack. It's used as a means to keep the enemy's head down in order for us to get away, or keep the bad guys off the good guys for a few seconds. Using full auto highlights your position, will 99% of the time not hit your target, and is a waste of ammo. If you're concerned with having a full automatic weapon for the purpose of self-defense, especially a crisis situation, it's not going to help. In fact it will likely do the opposite, by making you the #1 target, running out of ammo early in a firefight, and/or degrading the gun's accuracy due to heat (only machine guns are designed for continuous, sustained automatic fire).
If you're planning on room clearing (which I doubt), that's the only reason I see fully auto becoming useful, and only for smaller sub-machine guns. In the open or urban environment, which will be the two most likely places in a SHTF situation, nothing beats sound tactics, and some well placed shots. If I'm across the other end of a field or alley, and somebody opens up on me with a full-auto rifle, I'm dropping to the ground, and firing 2-3 well aimed shots. Having such a low profile makes it very hard to hit me, especially on full auto. On the other hand, I know exactly where they are, have a more stable shooting position, and can easily get many well aimed shots down range with a good optic. It's kind of like the sideways grip. Bad guys stock up on illegal full-auto weapons. Will it help them? No. I'd rather face a mafia spraying and preying with AK-47's, than some tactically sound mob with good sharpshooters and optics.
Burst fire is sort of a gray area. It's very useful if you can control it, but once again it comes down to bringing your target on sight quickly and effectively.
Machine guns are a whole different area, because they're designed to fire accurately, fast, and with the ability to change out barrels on the spot. Assault rifles on full auto are mainly used for suppressive fire, and very rarely used on an attack (planning an ambush?).
If you're in a situation in which you need suppressive fire, and don't have a full auto, you can still bump fire your weapon to get the enemy's head down. Not a tactic I particularly recommend, but it's an option so you can get away.
Before you decide to invest in one, I strongly recommend going to a machine-gun convention, or a range that allows full auto (most ranges, including military, have dedicated ranges for full auto, and very strict rules regarding using them). Set up a target 50m away (close for an AR engagement), and run a mag through. Controlled bursts, full-auto, etc. See how many rounds actually hit the target.
I'm all for 2A rights, but I don't believe that means everybody has a right to own whatever they want. A legalization of class-III weapons for the general public on a wide scale, will just make those random mass shootings even worse (I almost sound like a gun-control freak, lol!). It puts us as open and concealed carriers at a severe disadvantage, unless they decide to let everybody walk around with a full-auto rifle, and that's not the type of America I want to see in the future.