Your not wrong, but you seem to be missing one significant detail: we have altered the biosphere even more by not engaging in nuclear activity, instead opting for less-scary-but-worse alternatives like coal, oil and gas.
"But what about the cobalt mines?" - that damage is limited in both space and time
For example if nuclear costs 1bn for a GW and solar+wind costs 0.6bn but you need to also install 0.5bn of storage to make the grid reliable to the safety margin you deem acceptable then it is no longer a cheaper system.
Amount of storage needed scales up rapidly as you get towards an grid with entirely intermittent generation.
Storage is more expensive than generation. Always.
We see some storage on the grid because storage is fast. Batteries can respond to load changes a lot faster than anything else. Demand goes up, the batteries are drawn down while cheaper generators are spun up. A few places use pumped hydro for the same purpose, but that's very situational.
The problem lies with the standard of As Low As Reasonably Achievable. If you had reasonably priced nuclear power you could add more safety. Thus you have to add more safety. Thus you no longer have reasonably priced nuclear power.
And, when it comes to power it's a totally wrong standard. You should not be looking to minimize individual technology risk, you should be looking to minimize total risk of competing technologies. Making your nuclear plant safer instead drives generation to natural gas (~10x as dangerous as nuclear, plus climate effects) and oil (~10x as dangerous as natural gas, even more climate effects.) Or even coal (~10x as dangerous as oil, even more climate effects plus nasty stuff going up the stack--including emitting more radiation than would be tolerated for a nuclear plant.)
I also think we should build more nuclear. I've seen estimations saying we could supply the current grid demands with renewables in about 10 years time if we start building now. Thing is, in ten years, power demand will have doubled. So we should build renewables and nuclear. Any other plan will end up using coal oil and gas.
You imply that we could have made enough nuclear plants to replace coal, oil and gas and that would have prevented the effects of fossil fuel consumption.
That's not the case. It would have been entirely impossible to make enough plants to even replace coal and oil fast enough, and even if we did, electricity is only 25% of emissions.
The claim that lack of nuclear power is to blame for global warming doesn't hold up because even in a best case scenario, nuclear power can only replace a small part of the activities that cause global warming, and it takes way too long to even replace that.
The argument that we have a choice between nuclear power or global warming is therefore either misinformed or dishonest.
We're already dealing with global warming, and as of 2026 the fastest, cheapest and most effective way to replace fossil fuel is solar power and batteries, not nuclear power.
Batteries are so far mainly deployed in cars, where they replace millions of gallons of fossil fuels from being consumed every day, but they can also effectively be deployed in homes, communities and cities. It takes days to deploy, can be mass produced and distributed to any country in the world with no issue (even North Korea and Iran) and immediately reduces fossil consumption.
Newly deployed solar panels are adding several nuclear power plants worth of new power to the world every year, and they too start working the same day and can be deployed by almost anyone, everywhere.
If we want to stop altering the biosphere by burning fossil fuels, clearly we should hurry up with batteries and solar and not spend billions and decades on nuclear.