It is misleading to claim current generation plants are safe, for all relevant meanings of safe. If they were actually safer than other power sources, the plants would be insurable. You could call them safe if they did not pose a bomb proliferation risk. You could call them safe if cleanup after accidents was a well-understood and feasible process. You could call them safe if the risks did not reach to somewhere between hundreds of miles and the entire planet.

Safer nuclear power is not just about reducing the possibility of immediate death, which, of course can't be entirely eliminated. You still have risk to employees from non-radiological parts of a power plant.

What you won't have from safer nuclear power plants is the risk of spreading stuff like Strontium 90 over a wide area. That by itself is a very valuable goal that will vastly reduce the maximum downside risk and the cost of mitigating that risk.

Cost is part of risk, in the form of financial risk. Smaller, less expensive plants are less likely to become white elephants on rate payers' bills. They won't lead to To Big To Fail entities that may need bailing out because they are the custodians of a big nuclear mess.

Safety is multi-dimensional. People opposed to building more nuclear plants with current technology understand that. They want to keep their wallets safe AND their milk safe. They want to keep the value of their property safe. That's perfectly rational.