Why were enemy weapons as trophies so scarce?

The stuff that was valued as souvenirs, swords, flags, pistols, and so on, tended to be things that were not common Common things like rifles, bayonets, and helmets were not much prized. Only officers would have swords or pistols, and there were twenty or thirty enlisted men for every officer. Nor would front-line fighters have much of an opportunity to wander about the battlefield looking for stuff. Immediately after an action, they'd be digging in and preparing to be counter attacked or sent to a base area to rest and refit.

Sledge actually explains in his book that they did not take rifles for rifles were to heavy to carry around; they only cared for light stuff like pistols or special knifes/swords and those were only carried by officers so there were by far not enough of them around for everybody.

As already stated, anything you have to pick up, you have to carry. There were also rules about bringing back war souvenirs. They showed teeth looted, but there were also many skulls brought back. Searches were conducted on the ships returning to the states, where no contraband was safe from seizure. Some ships were more lax than others.

Then you have to understand a little how the military works. Because of logistics, (and internal politics), there are always fewer real combat troops that actually see combat than those that don't. Not sure what the Marine stats were in the Pacific during WWII, but the Army stats in Europe have been arguably stated as being as low as 29% - Only 29% saw real combat on a regular basis, while the rest were units kept in the rear or support. The guys in the rear wanted things to bring home, but had a hard time getting to the front lines for the opportunity.

In Grenada we had issues with guys trying to take AK's back, and an Admiral was the highest rank busted for it. The thing about it, the support type guys were the main ones wanting the crap - nobody I was with wanted to bring an AK home - they were old and wore out. It's not like you could walk around with an AK on your back either, lol. At the tail end of every conflict there will be a mass migration of military people, that have spent the whole time in the rear or stateside, trying to make a short trip to the conflict area, so they can have the conflict added to their dd-201 file. It's the closest thing to getting credit for something you didn't do.