Explain which part? Why AAU membership is still a requirement to join the conference? Or why AAU membership got tied to conference membership in the first place? The answer is simple for both.
The Big Ten Academic Alliance (formerly named the Committee on Institutional Cooperation) was formed in 1958, including all existing conference members and the University of Chicago (a founding member of the conference who withdrew in 1946). At the time, inviting just the conference members was likely just out of convenience. There was likely already cooperation between the schools at the time and this just formalized it a bit more.
Why did they do this? Because at the time, sports were not a money maker for the universities, research grants were. So if sharing research access, among the other things the CIC enabled, meant more research grants from the government then it made a lot of sense to do.
At a certain point, the decision was likely made to make AAU membership a requirement to join the conference as a full member. Why? Because any school joining the conference would want in on the CIC, and as the existing members you don't want to dilute the quality of the research shared.
So what started as likely a decision of convenience, turned into a requirement for new members.
As for why it's still a requirement, it's also simple. Research STILL brings in more money to the universities than athletics. Each year, Big Ten Academic Alliance schools engage in $10 billion in funded research. Compare that to the $880 million in revenue the conference made from athletics. Research brings in more money by a factor of roughly 10:1.
You may ask "Why not just split the 2? Make joining the conference as a full member for sports not automatically grant membership to the academic alliance.". While that is a potential route they could go (and should athletics ever surpass research in the money that it brings in to schools, almost certainly a route that will be pursued), at the moment it's too much hassle. Any school considering joining the conference for athletics is likely going to make sure academic alliance membership comes with, because it means a lot of potential research money, and will likely make it a deal breaker. Further, if we admit someone, and then try to revoke their membership in the athletic alliance that is just begging for a costly lawsuit to happen (and is likely at least part of the reason Nebraska was not kicked from the academic alliance when they lost AAU membership).
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