Nalioth, you are thinking of the HKG11 caseless rifle in regards to the burst increasing ROF. Everything else HK makes with a burst trigger pack is same ROF as FA. On the G11 the mechanism recoils inside the outer casing, in FA mode the mechanism makes a full back and forth cycle before the next round is fired automatically. When the burst mode is selected it fires 3 times during the rearward stroke, the last bullet has left the muzzle before the recoil impulse is really felt. On their conventional cased ammo rifles the ROF is limited by the speed the bolt can cycle. As the bolt closes on FA it trips the auto sear and drops the hammer to fire the next round, in burst mode a ratchet mechanism "counts" however many cycles it is made to limit and stops the hammer fall after that limit is reached, then resets on trigger release. If your average MP5, for example has a FA cyclic rate of 633 RPM in order for it to hit 2,000 you would have to speed up the bolt cycling to 3 times faster. I dunno how a trigger group could do that.
The caseless G11 is capable of 2,000 RPM because the mechanism only loads and fires the cartridges, no extraction or ejection needed so it's very fast. They actually slowed the FA mode down so it would be more controllable and conserve ammo.
The standard HK burst mechanism is much superior to the M16, it resets itself back to zero even if less than a full burst is fired. The M16 does not, if you stop a burst shy of 3 it will fire the rest of the burst on the next trigger pull. From what I understand it also makes the trigger pull suck, in semi auto the burst mechanism is still active so each succesive pull feels harder until it resets every third shot. Read a report somewhere that some marines were breaking their burst mechanisms to get better trigger pull and accuracy in the sandbox.