Look, even as there might be general agreement among the people to fight climate change, there might be little to no agreement among the people as to how to actually proceed doing that. Because of this, you cannot say that blocking EPA here is undemocratic, because “ majority of the US population wants regulations to fight climate change”: it is very much untrue that majority of people want the exact policy that EPA tries to introduce, and have it be executed by EPA. It’s like saying that majority of US population want regulations to improve their commute times, so SCOTUS cannot block DoT from eminent-domaining land through cities and building 10 lane highways on it. Some people want that, sure, but others want more trains or zoning regulations to improve walkability, and there is no majority agreement here on the details of the policy. You certainly don’t want unelected bureaucrats with no accountability to voters be deciding major issues like that.
In an environment with as much epistemic uncertainty as climatology has, it is madness to allow bureaucrats to control anything at all. They are in no way fit to make important decisions on scientific topics.
At this stage in the climate crisis, we really need to be focused on direct results of political actions. The majority of the US population wants regulations to fight climate change, and the consensus among climate scientists is that if we don't aggressively cut carbon emissions immediately, things will get really out of hand. Therefore, if the Supreme Court is reducing the EPA's ability to help this, it is both anti-democratic and massively harmful to the public good. It really doesn't matter that the EPA is executive overreach according to some document written 230 years ago.