A lot of the material in the drums isn't dangerous by itself - it is just contaminated with dangerous material. At my workplace, we fill drums full of used protective gloves, used facemasks, and used hazmat smocks. A five-gram glove might have only 0.005 grams of chemical on it, but the whole glove has to get discarded as hazardous waste.
Hazardous waste disposal companies might pay to have this waste concentrated. Instead of storing a thousand drums of mildly hazardous materials, it would be cheaper and easier to store a single drum of hazardous materials. It's easier to watch a single drum and keep it from leaking than to watch a thousand drums, so safety would be improved. It would be interesting to do this, and would be a good way to create jobs.
To start, a drum of waste would be emptied into a glove box, or spread out under a fume hood (depending on what was in the drum). Workers would visually inspect the contents and separate them. Next, a technician would identify what could be done with each group of items.
Glassware contaminated with chemicals could be scrubbed clean with water and solvents. The glass would then be safe to put in regular landfill or recycling, while the dirty solvent could be distilled and reused. The small amount of sludge from the distillation process would be the only bit left to put back in the toxic waste drum.
Contaminated paper wipes could be soaked in something like muratic acid. The paper would dissolve, and the solids left behind would be what you'd put back in the toxic waste drum. The liquid could be distilled to be re-used, and the sludge left behind would be safe to dispose of in municipal landfill.
Contaminated plastics could be put in a chamber with high-pressure superheated steam. Most material would break down to hydrogen and carbon monoxide (which you would extract and flare off); the residue would be put back in the toxic waste drum.
The initial sorting would be very labour-intensive, and probably would only make sense to do when times are tough and people will work cheaply. That's fine - the hazardous materials aren't going anywhere. When the economy is booming and there are jobs, you can let the low-level waste pile up. When the economy tanks, you've got jobs for people who would otherwise be unemployed.