Most needles come in single use packages. They are so cheap it doesn't matter.
But it's not the Death Row Inmate they are protecting, necessarily. It's the staff adminstering the injection. If they were to slip, or jab themselves accidentally after giving the injection - the only person they need to check for disease is the DR Inmate's corpse (and themseves of course).
If it was unsterilised...they could be accidentally giving themselves a death sentence.
As a nurse, I'd rather the needles were sterile thanks.