If your goal is to free academic publications, can you clarify as to why it's necessary to register for an account to download papers from academia.edu?
Anyone can read the entire article in the browser on Academia.edu without logging in or registering. The paper is displayed using HTML5 in the browser, and there is no need to register to read the full text of the article.
We require people to register if they want to download a local copy of the paper. Registering takes a few seconds, and is free. Our users don't mind doing it.
Academia.edu's philosophy here is somewhat similar to BitTorrent's. With BitTorrent, if you want to download chunks of a file, you need to be uploading the same chunks to other people, and that is how the content and the community is sustained.
By requiring people to register to download articles, scientists are more likely to come back to Academia.edu and upload their own articles, increasing the number of open access articles on the web in general.