The poor countries cannot buy or sell products. Their economies shut down. Their workers become unemployed. Food products vanish. Medicine and health care products disappear.
Sanctions can kill more people than actual warfare.
But the rich countries can kill the people in poor countries without putting their own soldiers at risk. The U.S. has used sanctions and regular bombing of Iraq for nine long years. More than one million Iraqis have died. Those responsible for this policy should be put on trial for crimes against humanity and war crimes. This is terrorism, plain and simple.