"but why hasn't EA done this already?"
still seems like a fair question. I think the underlying problem you're pointing to might be that people will then give up on their projects or ideas without having come up with a good answer. An "EMH-style" mindset seems to point to an analytical shortcut: if it hasn't already been done, it probably isn't worth doing. Which, I agree is wrong.
I still think EMH has no relevance in this context and that should be the main argument against applying it to EA projects.
I had to use Wikipedia to get a concise definition of EMH, rather than rely on my memory:
The efficient-market hypothesis (EMH) is a hypothesis in financial economics that states that asset prices reflect all available information. A direct implication is that it is impossible to "beat the market" consistently on a risk-adjusted basis since market prices should only react to new information. 
This appears to me to apply exclusively to financial (securities) markets and I think we would be taking (too) far out of its original context in trying to use it to answer questions about whether great EA projects exist. In that sense, I completely agree with you that:
it's a poor way to model the situation that will lead you to make systematically wrong judgments
In the real (non-financial) world, there are plenty of opportunities to make money, which is one reason entrepreneurs exist and are valuable. Are you aware of people using EMH to suggest we should not expect to find good philanthropic opportunities?
Should we also link out to https://80000hours.org/podcast/effective-altruism-an-introduction/ as an alternate way to consume similar content?
I don't see the connection between EMH and EA projects. Can you elaborate on how those two intersect?
What is the relationship between this handbook and the one hosted at https://www.effectivealtruism.org/handbook/ ?
The handbook at the above link is available in epub, mobi, and pdf formats, which seems to answer the requests in the comments here. Is it an older version? The cover indicates that it is the second edition, but sadly does not include a revision date.
It looks like the EA Pen Pals project is closed for lack of funding.