Breakthrough Institute works like the Copy Protection technology wizards selling their tech to record companies. It cannot work, because the pirates will always find a workaround towards copy protection - you are merely punishing your customers and training them to be pirates when they try to use your product in convenient ways. The Copy Protection technology wizards are not selling a working solution - because a solution is impossible - they are selling a pleasant fantasy to the record companies in the few years their business model has left.
People do not confine themselves to buying working products. Sometimes they will purchase fantasies. Look at the exercise gizmos that people buy from TV.
The Breakthrough Institute doesn't have to provide solutions that work - it will provide fantasies that it can sell. So lets try and figure out who their customers are.
If you are in the top 0.5% of incomes, you are intelligent and you may be slightly distressed that your great grandchildren will be born into a boiling world (when you can be bothered to consider the issue). You have the ability to direct funding, and in these few years before the climate disruption really hits human agriculture and infrastructure, you are in the market for fantasies, sold to you by the semi-knowledgeable folk (who are probably sincere, because their confidence in their tech solutions surpasses their scientific capabilities). That is what people like the Breakthrough Institute are selling. For example, Warren Buffet doesn't consider himself a bad person, and he cares for his grandchildren. But he has also made a huge bet on coal transport infrastructure. He would love to support the Breakthrough Institute by some means, to reconcile his position on the responsibility of environmental stewardship for future generations.
"The Breakthrough Institute, a project of Rockefeller Philanthropy Advisors, Inc." lets you know about the customers they are after. How did good ol' John D. make is money?
Lets predict their structure. They will rarely speak in absolute moral terms - they will never flatly state that it is craven to leave future generations a boiling world just because a handful of generations could not bare to lower their standard of living. The absolute moral issues will always be left unspoken. Those that talk about the moral issues will be marginalized as "un-serious" or "alarmist".
They will strive to distance themselves from the worst of the denialists. Pielke Jr and Fuller practically fell over their own feet trying to run away from Virginia State Attorney General Cuccinelli. But they will take "warmist" commentators that have a record of limiting themselves to the published science, like Romm, and equate them with denialists that spout off bat-shit nonsense - even thought the implication of equivalence is ridiculous. But you will know them by their actions, because they will spend most of their energy arguing against those with the clearest grasp of the facts, and moral issues, and political challenges.
It is the foolish "moderate" position of shifting your stance a few inches when you are standing on tracks, freight train coming. The half measure doesn't leave you just half-dead.
All you can do is make the case to ethical decision makers that they are being sold a bill of goods, by comparing the statements and techniques and rhetorical stances of the Breakthrough Institute to bunglers that stood in the way of decisions of moral courage, and the weavers of the Emperors New Clothes. These are the "moderate" apologists for moral failures - like those who stood in the way of eradicating slavery, or were the audience for the Letter from a Birmingham Jail, or were willing to negotiate with Hitler, or were willing to overlook Stalin's crimes. In all these cases, you could find "moderates" that participated in moral failures, and argued for positions with shabby facts and shabby rhetorical devices.
Moe, Rockefeller is the BTI fiscal sponsor; the main funder throughout has been the Nathan Cummings Foundation. By itself the fiscal sponsorship doesn't mean much,although it may well in this instance.