Well, good news, the topic of getting rationality into academia is something I'm actually working on myself as an academic. For example, I just published an op-ed in one of the most premier higher education media channels on how I as a professor used rationality-informed strategies to deal with mental illness in the classroom. Earlier, I published some research informed by rationality concepts, such as agency.
As part of my broader project of promoting rationality widely, I'm also starting up a research project on debiasing the planning fallacy using rationality-informed strategies and on finding life goals using rationality strategies. I'm planning to publish research papers on these topics, naturally.
So I'm guessing some of the reasons why rationality is just beginning to enter mainstream academia is because of the very long cycle of conducting research and then publishing. Another set of reasons has to do with academics like myself taking time to figure out how to integrate rationality into their research fields.
I feel that a lot of what's in LW (written by Eliezer or others) should be in mainstream academia. Not necessarily the most controversial views (the insistence on the MW hypothesis, cryonics, the FAI ...), but a lot of the work on overcoming biases should be there, be criticized there and be improved there.
For example, a few debiasing methods and a more formal explanation of LW's peculiar solution to free will (and more, these are only examples).
I don't really get why LW's content isn't in mainstream academia to be honest.
I get that peer review is not the best (far from it, although it's still the best we have, and post-publication peer-review is also improving, see PubPeer), that some would too readily dismiss LW's content, but not all. Lots would play by the rules and provide genuine criticisms during peer-review (which will lead to the alteration of the content of course), along with criticisms post publication. This is in my opinion something that has to happen.
LW, Eliezer, etc, can't stay on the "crank" level, not playing by the rules, publishing books and no papers. Blogs are indeed faster and reach a bigger amount of people, but I'm not arguing for only publishing in academia. Blogs can (and should) continue.
Tell me what you think, as I seem to have missed something with this topic.