So in my head I was comparing the Church to, say, communism, which is where I got the "absurdly good" idea. Communists killed roughly 5,000 times as many people as the various Catholic inquisitions. But in retrospect that wasn't a very fair comparison, and so I repent of it. Mea culpa.
What obvious reasons?
If the Catholic Church tried to kill heretics in modern times, it would first have to declare war on the entirety of the United Nations. ...Surely it is clear why this would not accomplish anything useful.
Question: if you somehow time traveled back to 1491 and the pope asked you whether he should endorse a new Inquisition in Spain, would you tell him yes?
Reservedly but emphatically yes. I suspect the Church's involvement in the Spanish Inquisition, however limited, saved many lives and prevented costly wars.
I'm curious if you've read Pinker's "The Better Angels of Our Nature". A major part of how humans have become less peaceful is that we're less willing to kill over ideas, whether those ideas are religious or ideological in nature.
I'm skeptical about trying to build FAI, but not about trying to influence the Singularity in a positive direction. Some people may be skeptical even of the latter because they don't think the possibility of an intelligence explosion is a very likely one. I suggest that even if intelligence explosion turns out to be impossible, we can still reach a positive Singularity by building what I'll call "modest superintelligences", that is, superintelligent entities, capable of taking over the universe and preventing existential risks and Malthusian outcomes, whose construction does not require fast recursive self-improvement or other questionable assumptions about the nature of intelligence. This helps to establish a lower bound on the benefits of an organization that aims to strategically influence the outcome of the Singularity.
(To recall what the actual von Neumann, who we might call MSI-0, accomplished, open his Wikipedia page and scroll through the "known for" sidebar.)
Building a MSI-1 seems to require a total cost on the order of $100 billion (assuming $10 million for each clone), which is comparable to the Apollo project, and about 0.25% of the annual Gross World Product. (For further comparison, note that Apple has a market capitalization of $561 billion, and annual profit of $25 billion.) In exchange for that cost, any nation that undertakes the project has a reasonable chance of obtaining an insurmountable lead in whatever technologies end up driving the Singularity, and with that a large measure of control over its outcome. If no better strategic options come along, lobbying a government to build MSI-1 and/or influencing its design and aims seems to be the least that a Singularitarian organization could do.