Because it makes no sense, environmentally or economically speaking. Nuclear is, as you said, base load. It can’t adjust for spikes in demand. So if there’s more energy in the grid than needed, it’s gonna be solar and wind that gets turned off to balance the grid. Investments in nuclear thus slow down the adoption of renewables.

Solar is orders of magnitude cheaper to build, while nuclear is one of the most expensive ways to generate electricity, even discounting the waste storage, which gets delegated the the public.

Battery technology has been making massive gains in scalability and cost in recent years. What we need is battery arrays to cover nighttime demand and spikes in production or demand, combined with a more adaptive industry that performs energy intensive tasks when it’s abundant. With countries that have large amounts of solar, it is already happening that during peak production, energy cost goes to zero (or even negative, as traded between utilities companies).

About the heating: gas can not stay the main way to heat homes, it’s yet another fossil fuel. What we need is heat pumps, which can have an efficiency of >300% (1kWh electricity gets turned into 3kWh of heat, by taking ambient heat from outside). Combined with large, well-insulated warm-water reservoirs, you can heat up more water than you need to higher temperature during times of electricity oversupply, and have more than enough to last you the night, without even involving batteries. Warm water is an amazing energy storage medium. Batteries cover electricity demand as well as a backup in case you need uncharacteristically much water. This is a system that’s slowly getting adopted in Europe, and it’s great. Much cheaper, and 100% clean.