This is a messy subject, and one that's difficult write about, and I appreciate you tackling the topic. I think there are some important qualifications to make about this post, as others have noted. But I know that when writing about messy subjects, it's hard to avoid "death by a thousand qualifications." Lately, I've been trying to solve the problem by putting most qualifications in footnotes, e.g. here. You might want to try that, as it mitigates criticisms of the "but you didn't make qualifications X and Y!" form while still leaving the body text in a readable condition.

Below, I'll refer to MWA ("many weak arguments") and ORSA ("one relatively strong argument"), for convenience.

Here's my guess at what's going on:

1. Probability theory doesn't "intrinsically favor" MWA over ORSA. Both have their uses, their limits, and their "gotchas" when applied to bounded rationality. If MWA is in some important sense "reliably better" than ORSA, I'd need stronger evidence/argument than is provided in this post. (That's not necessarily a criticism of the post; putting together strong evidence+argument about messy subjects is difficult and time-consuming.)
2. For historical reasons, Less Wrong tended to attract people accustomed to ORSA thinking — which is common in e.g. mathematics and philosophy. Hence, LWers tend to make "too much reliance on ORSA"-type mistakes more often than they make the "too much reliance on MWA"-type mistakes.
3. Givewell tends to emphasize the MWA approach, and has been remarkably successful at figuring out the parts of the world they're trying to understand. This impressed you, and helped you to realize that, like many mathematicians, you had been placing too much emphasis on ORSA thinking.