The more intrusive spyware they force-feed gamers in the form of DRM and/or digital distribution, the more will acquire their copy from Piratebay instead. Further, any and all copy protections have been cracked or will be cracked, it's just a nuisance that alienates paying customers, nothing more. Of course, if EA Origin is indeed what the EULA claims, that steps way, way over the line.
I really hope someone challenges the provisions of that EULA in a court of law here in Europe - we already have had several cases where a US-written EULA has been declared by a court to be null and void outside the US when it comes to conditions prohibiting reselling, modifying, reverse engineering, etc. Demanding the rights equivalent to a police search warrant in exchange to allow the use of a software is certainly unreasonable. Unfair terms and conditions are automatically voided, so all it takes is one brave individual who can prove that the EA spyware snoops around his computer and takes this to a court, and at least us Euros will probably get a toned-down version of EA Origin as a result.
By the way, how does one differentiate "illegally downloaded material"? There once was a lulzy software that was distributed by the local arm of the copyright mafia, advertised to parents concerned of their children's net usage. What the program did was to simply uninstall all p2p programs (because, you know, torrenting eg. FH2 must be illegal) and then proceed to delete all sound and video files not protected by DRM (this was before even iTunes started selling, whaddyaknow, unprotected mp3's).
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That said, I cannot understand why I should be forced to install bloated spyware on my computer if I purchase a physical disc copy of a game. So far, my honestly purchased Duke Nukem Forever has been laying in my bookshelf because it tries to force-feed me the Steam. Oh well, maybe I'll just download a pirate copy that certainly does not require Steam.