Frankly, i think that aliens DONT want that their weapons, ships and other technologies go to human hands. As in the same way one country dont want to see that his technology go to another one.
Thats why the aliens would have autodestruction ships, weapons, or maybe chemistry reactions for desapear his own bodies, databases autodestruction, and others...
When completing a mission, is must preffer that not all that technology go to human hands. If the alien ship smashed, or shoot down probably a lot of the technology of the ship will be lost, many of the aliens and their weapons will be lost with the soldiers shoots (If you shoot a rocket launcher, a granade, a plasma rifle or another kind of weapon to a alien, what would happen with the weapon the alien is carry?).
And the alien technology required for experimenting, those requirement would be lost!. (Because they fail in some of their experiments, or they need those items for future experimenting purposes).
OR NOONE WILL PRODUCT HIS OWN TECHNOLOGY.
Remember that Phalanx team isnt a tipical team (they have a really short number). With 8 weapons stealed form aliens you can have YOUR COMPLETE group equiped with those weapons.