We normally think of heroic responsibility as a good thing. It is what heroes do: they take responsibility for getting the job done, saving the world, protecting the innocent. They do what it takes, even though it's not their job, even though society might be actively pushing back. That's why they're heroes.

You know who else does that? Villains. The James Bond villain who has decided that he, yes he, is going to build an international criminal organisation complete with volcano lair, in order to overthrow the world order and obtain immense wealth? He also took heroic responsibility. He decided that he wanted to achieve an audacious goal, he demonstrated the determination necessary to drive it to (near) completion, he wasn't discouraged by social disapproval, he didn't wait for someone else to give him his hero license.

In non-fictional examples, we see heroic responsibility among activists and people who pioneer social movements. Sometimes this is a wonderful thing. Martin Luther King could have decided that he was just one minister in one church; it wasn't his job to convene and lead a national civil rights movement. Instead, he took heroic responsibility, and made America a better place. But equally, it can be a terrible thing. Osama bin Laden could have decided that it wasn't his job to lead the global jihad against the Great Satan. But he took heroic responsibility, founded al-Qaeda, planned the 9-11 attacks and the murder of thousands of people, and thereby provided the casus belli for the Afghanistan war and yet further loss of life. 

Sometimes people demonstrating heroic responsibility can be directly opposed to one another. Consider: the founders of the YIMBY movement took heroic responsibility to try and lower house prices. But every NIMBY who's decided they are going to do whatever it takes to block that development is also taking heroic responsibility. Devout Christians who decide it's up to them to found churches or launch international missionary projects display heroic responsibility no less than Anton LaVey founding the Church of Satan, or Eliezer Yudkowsky founding the rationalist movement. 

Heroic responsibility can be immensely powerful, but it remains morally neutral. Whether in yourself or others, please think about whether the goal is right before you cheer on the high-agency person doing what it takes to achieve it.