Actually, the glut of donated supplies following a tragedy is such an ongoing problem that emergency workers have a term for it -- they call it "the second disaster."
After the Sandy Hook school shooting in 2012, in which 20 primary school kids were fatally shot by one human garbage fire for no reason, well-meaning citizens mailed upwards of 67,000 teddy bears to the surviving children. We're not sure exactly how many kids these bears were supposed to be distributed amongst, and we're not exactly child psychologists, but we're guessing that if a child's trauma can't be alleviated by the sudden appearance of 10 teddy bears, then an extra 1000 teddy bears per child probably has no added therapeutic benefit.
On top of that, Sandy Hook's surviving victims drowned under thousands upon thousands of donated toys, bicycles, clothes, and school supplies. Literal tons of stuff ... all of which has to be stored, sorted, and disposed of once every affected family no longer has room to fit a 265th used Tickle Me Elmo in their home. You know what didn't get donated? The money and manpower to sort through all of it. So, the vast majority of the stuff wound up in a dumpster, because care workers don't have time to re-donate all that stuff back into charity when they, you know, have a bunch of traumatized kids to look after.