1) Energy investment is primarily driven by cost, not perceived/actual safety. Safety regulations do affect cost, but not enough to significantly change investment (at least in the US, with the current conditions).
2) Base load power and intermittent (e.g. solar/wind) power are not the same thing, and are not comparable. The concept that "solar and wind will save us all" by themselves is fundamentally incorrect, and actually they make things worse in many ways.
Nuclear fear mongering has resulted in high levels of regulations around nuclear power, but even without that natural gas has an edge in $/kWh. There just hasn't been demand to build nuclear. On top of that, nuclear needs to run 24/7 to amortize high capital costs. With solar/wind, there is high variability in grid supply, so nuclear is significantly less cost effective, and is getting phased out in favor of low-capex plants (i.e. natural gas).
Barring some energy storage miracle, we'll eventually end up with ~35% renewables, 15% hydro, 50% natural gas in the US, with HVDC interconnect. No nuclear, no coal.
(source: I work in a Climate and Energy R&D group)