Why does academia.edu reserve the right to sell, modify, and "exploit" my papers if I post them there?
It's not necessarily crazy for academia.edu to ask for these things (although, as I say below, I certainly don't think users should agree to these terms).  I imagine their lawyers advised them to use an agreement that covers all possible use cases as their business model evolves.  For example, if they decided to charge their users membership fees, and only users who paid the fees got access to the site and could view profiles and download papers, then that would be tantamount to selling the papers and other user data (so they couldn't do it unless they had permission to sell this content).  Posting ads on their web pages could be considered a form of commercial exploitation of the data, so they want to make sure they can do it.  They might someday want to change file formats, such as converting PDFs into future super-PDF formats, and having permission to modify content submitted by users guarantees that they could do this.  Even if they intend to take things down upon receiving requests from users, having irrevocable permission to post them means users cannot sue them for failing to take them down quickly enough.  Basically, this agreement says they can do anything they want, which is obviously very convenient for them.

For comparison, Harvard's model open access policy also retains very broad rights (although not the right to sell papers for a profit).  I believe the motivation is that universities can be trusted, and it's better for them to retain more rights than fewer, in case they need them someday.  See the notes to line 7 in the model policy for more discussion of this point.  Of course, the difference is that academia.edu is a commercial website, and even if they are trustworthy now, they might become less so in the future or be bought by someone untrustworthy.

On the other hand, even if it's not crazy for the site to ask for these rights, it's certainly crazy for users to agree!  I'm amazed that these terms of service are being used, and I assume just about nobody using the site has actually read them and understood that they are permanently granting the right to sell arbitrarily modified versions of their papers.  I hope you send them a complaint, as well as publicize this on the internet, because they need to change these terms as soon as possible.  In addition to being completely unreasonable, they clearly conflict with a large majority of copyright agreements for papers, as you point out.