Here's a video where an energy professor goes through the finances of gas vs nuclear power (very slowly) - https://www.youtube.com/watch?v=cbeJIwF1pVY

In short, it takes a very long time for a nuclear power plant to become profitable. Investors would rather pick something like gas that starts being profitable earlier, so they have the profits available to reinvest into other enterprises.

I think this, rather than public perception, is why we don't do nuclear power (after all, our society does plenty of other things despite similar levels of outcry).