Nuclear is not used for any of those either. And to use nuclear for heat and transport the easiest way is to just turn it into electricity and use EVs and heat pumps. So we're back to how to clean up electricity.
Cleaning up the grid isn't just useful for the immediate emissions benefit, it's also because if you concentrate the clean technology there you can decouple the problem and clean up everything else by electrifying. There are things like fertilizers and steel where we have more than just the energy input to clean up and even those have solutions based on electrification.
Sometimes, nuclear is used directly for heating by distributing heat to district heating systems.
We have electric cars on roads being sold in massive numbers.
We don’t have cars with little nuclear reactors sitting inside them.
So how is transport a good example of something that would somehow be better solved by nuclear than solar/wind?
Cars will charge from the grid. Nuclear can output not only a lot of energy but output it at a const rate. Wind and solar cannot do that. There are times when wind isn't blowing and sun isn't shining. There are entire seasons when wind and solar output is lower. There are multiple years where wind output is lower. That variability also means you need to over build capacity. But even with that, you're still in trouble because there is no battery technology now, or coming out anytime soon, that can store enough energy (minimum of a few weeks worth) to bridge that intrinsic variability of daily, as well as inter and intra annual variability.
Hell, let's not forget that the current plan is for people to charge their cars at night. That's when my car is plugged in; during the day I'm either parked at a public garage, or, you know, driving it around. Sure, there's probably still wind, somewhere, at night, but you're still charging your cars when your renewable energy sources are at their minimum.
The obvious solution for that is for people to plug in at home or at their job - chargers cost less than $500 (that includes installation costs), so it's not entirely impossible for workplaces to install one charger per employee and charge a margin on top of electricity prices to recoup prices. This will be desirable for EV owners once daytime electricity is cheaper than nighttime electricity, and therefore profitable for any location-owners to install.
If you have a car with ~600KM of range, then considering people drive an average of 60KM/day, you can imagine that most of the time most people basically don't need 90% of their battery and can wait until the next day. And considering people only use their car for an average of (IIRC) 2 hours a day, most of the time peoples' EVs will be idle for the charging somewhere.
For special roadtrips that might change, and perhaps midnight EV charging will spike on boxing day or such, but for the other ~360 days of the year people will largely be charging with solar.
Also, as serious as the issue is, let's remember we're talking about a projected ~5% increase on the electricity demand once the entire population goes electric. Over a decade that's less than 1% increase per year. That's not that hard, especially if we're planning to replace over half of the grid with renewables anyway.
You do know that weather happens and there are many days where solar output drops to zero or near-zero (think snow storm as an example).
We're talking about averages here. If solar is 10% cheaper then it doesn't matter if the price doubles once a fortnight.
It's a counterpoint to the claim that the transformation has already been achieved.
Even taking the example of Scotland (which is a doing rather well in this regard) electricity is a relatively small portion of energy consumption. Heat and transport are the dominant areas, and both are still mostly fossil-based.
https://www.scottishrenewables.com/our-industry/statistics