I'm reading Phantom Warriors by Gary Linderer which is about Long Range Reconnaissance Patrols in Vietnam. Good stuff. I'm only about halfway through but there seems to be a big deal about capturing enemy weapons. One of the team leaders just got chewed out by a G-2 Staff Officer for failing to take the weapons of 3 NVA that they had killed outright (who were the leading end of an NVA patrol). What was the big deal? I realize weapons are a valuable commodity, but to the point of taking the time to strip 3 soldiers who you know are at the front of a much larger force?
Also, I have previously read Slob by Rex Miller in which Daniel Bunkowski (homicidal maniac) is an enormous man and was loaded up with however much weaponry he could carry and was basically just released into the Vietnam jungle for periods of time to kill and wreak as much havoc as possible until he returned. If I remember right, there were other men/teams who were released as well. I think they basically had their identities scrubbed so the gov't didn't have to ever acknowledge they did that.
That's obviously fiction, but is there any real truth to that? Were small teams of soldiers ever just released in Vietnam with no other purpose than to kill?
Just to briefly talk about the capturing of weapons - this was sometimes done in conjunction with retrieving bodies to prove that you've killed an armed combatant as part of the body count system. However, like you mentioned, it seems illogical to do so if you are part of a LRRP and are working in close proximity to enemy formations. It wasn't entirely uncommon to retrieve weapons for intelligence purposes or to use them yourself, but the amount would be limited.
Now, was there any truth to small teams of soldiers with the only task of killing the enemy? Well, yes. That was the entire core of the American strategy in Vietnam, to search and destroy the enemy with superior firepower. This was part of a larger strategy of attrition where the belief was that if you killed enough of the insurgents, the insurgency would stop. While this might have been more suitable in a conventional war rather than a counterinsurgency conflict, this was what was chosen as a suitable strategy. The smallest unit to go out on patrols like these were platoons (since any smaller would have no chance against insurgents that could easily outnumber you). Even though it was far more common for the VC or NVA to ambush American patrols, the US forces always had ferocious fire support which gave them the edge if their enemies prolonged their attack longer than necessary.
The smaller teams, be it LRRP, Navy SEALs, Green Berets or SOG, usually worked on a more limited basis and focused on reconnaissance and intelligence collection as well as more conventional operations like ambushes, raids and other operations like it.