I don't doubt that you've used it with positive effects.
Here's a USDA study that concludes "This work has conclusively demonstrated that benzethonium chloride is present in commercial GSE samples. Higher amounts of benzethonium chloride were present in powder GSE samples than in liquid GSE samples, although we did not determine the exact concentration. This research confirms an earlier study (15) that found benzethonium chloride in commercial GSE samples."
That's a peer-reviewed study in the Journal of Agricultural Food Chemicals. Since they also site a study which states "However, only one of the six GSE samples tested did not contain any preservatives and this sample did not show any antimicrobial activity," I would conclude that you are in fact chlorinating your water with positive, beneficial results by adding the commercially available GSE to your water. Since the concentration of benzethonium chloride in the GSE is not consistent, I'll stick to products that are made for water purification.
Another reason I wouldn't allow scouts to purify water with GSE:
G2SS wrote:Treatment of Questionable Water
In addition to having a bad odor or taste, water from questionable sources may be contaminated by microorganisms, such as Giardia, that can cause a variety of diseases. All water of uncertain treatment should be treated before use. Don't take a chance on using water that you are not sure of. To treat water, follow these steps:
1. Filter the water to remove as many solids as possible.
2. Bring it to a rolling boil and boil it for a full minute.
3. Let it cool at least 30 minutes.
4. Add eight drops of liquid chlorine bleach per gallon of cool water. (Use common household bleach; 5.25 percent sodium hypochlorite should be the only active ingredient; there should not be any added soap or fragrances). Water must be cool or chlorine will dissipate and be rendered useless.
5. Let the water stand 30 minutes.
6. If it smells of chlorine, you can use it. If it does not smell of chlorine, add eight more drops of bleach and let it stand another 30 minutes. Smell it again. You can use it if it smells of chlorine. If it doesn't, discard it and find another water source.
7. The only accepted measurement of chlorine (or water treatment agents) is the drop. A drop is specifically measurable. Other measures such as "capful" or "scant teaspoon" are not uniformly measurable and should not be used.
In addition to common household bleach, several other types of chemical means to disinfect water are available, such as iodine tables, iodide crystals, and halazone tablets. All of these are acceptable, but some people have an allergic reaction to iodine products. Follow the instructions on the package for proper use.
To treat cold water you must lengthen the contact (sitting) time depending on the water temperature to destroy Giardia that may be present. Very cold water may take as long as four times the normal contact time.
Several types of water treatment filters are available at camp stores. The Boy Scouts of America recommends that if you use a water filter, you also chemically treat and/or boil the water and carry extra filter cartridges and spare parts. Among the best water filters are PUR, MSR, Katadyn, First Need, and Sweet Water.
You're not following the Guide to Safe Scouting.