Legal question: Does Origin display the EULA before you actually spend the money?
That's a question because here (.de) there's some ambuity regarding EULAs. Some argue that they are terms to the purchase contract and as such void when added after the contract is closed, some argue that that's a non-issue, because you can go back on that contract if you disagree with those terms... Fortunately, there's no ambiguity regarding the validity of some of those terms: If they are valid, they are general terms and conditions and as such to be evaluated under the General Terms and Conditions Law (here: AGBG). And that means that stuff that is "surprising" or "one-sided" is not part of the contract. (For details, contact a lawyer. I'm no lawyer!)
Well, whatever. Regarding Origin: I find it laughable that it took three of those platforms for anyone to actually notice that they have crappy terms of service. Why did we (as customers) let companies get away with that for such a long time? Much has gone wrong with the legal situation, both in the US and here, in the last two decades. The more laws regulated computing, the more rights customers lost. Fifteen years ago it was legal to make a safety copy of a game you bought. It was even OK to let them circulate in small numbers (IIRC it was as much as eight copies).
It was OK to break copy protections. (I still see it as OK in Germany, _if_ the copy protection prevents you from actually playing the game you rightfully bought!)
However, IMO there's so much else that's wrong with publishing... I'd rather support Valve and Impulse in their quest to make a better service and just hope that they give the money saved from not doing printed promotion, pressed discs and so on to the developers, who are the ones that actually deserve the money. But, well, that's just publishing, and you have the same problems in book publishing (just that there the deserving aren't called developers but authors).
Regarding "EA has better things to do than find pirates": You seem to hope for the Stasi theorem (i.e. so much surveilance generates too much data for EA to process... that's how the Stasi was at the end). However, processing power has increased dramatically and if they can make their software find copies of their games with the DRM removed and have it gather proof that will hold up in court, and make the lawsuit computerized, believe me, they will if they think it gives them more money than it costs. And since "piracy" scaremongers always pull far too big numbers out of their asses, that last condition will probably hold. (I really, really hate that term "piracy", because it was coined purely to make copy protection circumventers and copy right infringers sound like they're hurting people. As in, with a cutlass!)
One other thing: When Valve created Steam, that was great. When Impulse created Impulse, that was already redundand, but it was OK, because Steam needed competition. But now EA creates Origin just out of spite? And I seem to remember EA taunting Steam in the beginning, like "That'll never pay off!". Well, to quote Mahatma Ghandi: "First they ignore you, then they laugh at you, then they fight you, then you win." EA vs. Steam is currently in round 3.