ISS throws away 2.9 tons of trash into orbit

I wonder if they could add a trash launcher to the ISS. If some kind of spring or slingshot threw trash retrograde with sufficient velocity, there should be two advantages:<p>1) The trash would be put in an orbit with a lower periapsis, increasing atmospheric drag causing it to re-enter and burn up more quickly.<p>2) The orbit of the ISS would be boosted by dV of the trash, reducing the fuel required for the next boost.

Anyone know why they didn’t just keep it around, surely having a few old batteries and a bit more shielding around the ISS might have come in handy? Was it risky to keep them around or did the extra weight (even in a basically weightless environment) come at a cost to maintaining orbit?

why not push it out of orbit, away from earth?