Even the existing designs are vastly safer than what we've been doing.

Here's how I answer the most vocal critics of nuclear power generation, who are usually (but not always) white, suburban women with college degrees:

Question 1: How many people have been killed by nuclear reactor accidents in the US since nuclear power reactors started after WWII?

Question 2: How many people have been killed mining coal in the US in the 20th century, most of which was used for power generation?

Answer 1: Three, that I know of, at the SL-1 reactor in Idaho Falls, ID, in January of 1961.  Many nuke critics like to bring up Three Mile Island. How many people were killed by TMI? None. For some reason, the popular conception among supposedly educated people today is that TMI was some huge disaster. The only people who suffered a "disaster" from TMI were the news media, who had to find something else to talk about after TMI.

Answer 2: Over 100,000 coal miners died in the US in the 20th century in mining accidents. Go ahead, check it out in MSHA records.  If we add it up by "all mines" it's significantly higher than 100K. But for just coal alone, we're over 100K deaths from 1900 to 1999. 

Before WWII, it was not unusual to have over 2,000 men die in coal mining accidents in a single year. 

Then I like to play the sex card on the Karens yelling about nuclear power:

All three people who died at the SL-1 reactor were men. The vast, vast majority of that 100,000+ people who died mining coal were men.

From a man's perspective, it's a no-brainer that nuclear power is orders of magnitude safer than coal-fired power.