In vietnam there are photos of soldiers storing weapon lubricant, cigarettes, deet and various other items in their helmets. But even though the bands are still used up to today you never see them holding items in them. I'd assume it's due to stricter uniform regulations but I couldn't find an answer online.
Former (post-9/11) Soldier here. Mainly because with the introduction of Kevlar (as opposed to Vietnam-era steel) helmets do not require any sort of band to keep the cloth covering in place and were completely phased out over time.
During the time that helmet bands were available but not necessary (and were used solely to identify the Soldier or Marine to whom the helmet belonged, as the band had the Soldier or Marine's last name printed or written on it), the Uniform Code of Military Justice document that deals with uniforms and appearance (AR 670-1) had been updated to explicitly disallow the use of helmet bands to store anything with the exception of as a place to secure environmentally appropriate camouflage (leaves / branches for the most part). The latter was extremely rare as there's not much in the way of vegetation in the desert of Iraq or the mountains of Afghanistan.