It won't spread evenly across the planet. It will collect in clusters and hotspots which will never be mapped accurately, and it will make its way into the food chain, where it will be concentrated and eventually eaten, and where the Cesium and other long-lived decay products elements will eventually cause cancers, infant mortality and birth defects.

It won't kill everyone, but how many birth defects do you need before an area becomes marginally habitable?

People could move back to Chernobyl tomorrow. Most of them wouldn't die for years or decades.

That doesn't mean the Hot Zone is safe, or an ignorable thing.