My official opinion is that machine guns should be select fire (heavy machine guns, light machine guns, submachine guns, automatic rifles) absolutely, they are built for the very purpose and can handle full automatic and gain something from it. I posted elsewhere I would like, and may one day acquire, a semi auto no NFA stamp MG3/MG42, even without full auto. But damned if it doesn't really doesn't take a lot of potential out of the gun. Such guns are of the weight, build, caliber to be controlled on full auto, are used for suppression (save for SMG) that enjoys controlled bursts full auto offers, can maintain high rates of fire (save for SMG), are at their best at full automatic. The SMG handles full auto well and is best with it, skilled shooters who choose single shot aren't hurt with the option.
As far as battle rifles and assault rifles, that's a tougher one. Assault rifles can gain something out of it CQB as mentioned in this thread, sometimes close range controlled automatic has its place. As much as I don't like the AR so much, I do agree with the three round burst idea for the assault rifle, even at range it offers a controlled, single trigger pull burst to help improve hits and not a full on, burn through a magazine to accomplish nothing but burn the barrel idea. Civilian binary triggers can do something similar (if they aren't/don't get banned), the three round burst is good for close range as well. So, assault rifles do have something to be gained in certain situations, but then again full auto is a barrel burning ammo waster in ranged combat, taking it off may "idiot proof" the gun in some sense.
Battle rifles are interesting in the fact that Britain ACTUALLY fucking did it to their rifles. They took away full auto on their battle rifles out of choice to their troops. Wither this should be left as an option, wither this should be a matter of training and not taking away the option, is an interesting bit. But the fact a major world power did it shows you the nature of the rifle, standard battle rifles simply do not have the moxy to control the weapon in a meaningful way. To control the weapon, even in CQB, might just be better off with trained rapid fire single shot instead of a full auto string. Their firepower means they can do well without full auto, in theory, and especially in civilian cases, and have the least to be gained from full automatic because of control, even at closer ranges under combat conditions. I don't think the Argentinians gained an unstoppable advantage with full auto FAL's vs. the British rifles.
I classify purpose built heavy barrel rifles like the HB FAL and M14 variants to fit closer to the automatic rifle category than a battle rifle. Its intended for auto fire and as a support weapon, so more like the BAR. They are best off with full auto, of course.
And another point, as mentioned in battle rifle paragraph, in civilian and police situations where the Hague is off the table, the battle rifle will do very well without full automatic. If allowed to use soft points, the cartridges in battle rifles are almost guaranteed one stop shots, even minor hits can be crippling. The sheer advantage of firepower gained from increased terminal effect can offset the lack of full automatic fire. I have my battle rifles selected for home defense, even though the possibility is extremely low someone will attack, and I am not bothered by the lack of full automatic on my FAL, PTR, or M1a. Some of this is my capability, but also the fact that hunting rounds will render any crackhead useless with one or two shots with ease.
tl;dr I don't mourn the lack of full auto on my battle rifles, I would think heavily about getting a binary trigger for my assault rifles, and I am fucking sore about not having full auto capabilities on my subguns. I'm actually very upset about the possiblity of getting a MG3 like I want and not having it full auto. Reasons why are explained above.