Sony 'isn't' stupid. That's why EA Access isn't on PS4. Xbox fans might jump on board with EA Access, considering MS and EA's close relatioship going back years. But you just know if Ubisoft and Activision and 2K thought they could get away with it, we'd have 'Access' programs for all of them too and we'd have to sign up to like 5 services, thus leaving less games that would potentially turn-up on PS Plus/Games With Gold. Xbox are just desperate to look like they have a leg up on PS4 by having EA Access when Sony don't, but in truth EA Access sets a bad precedent for possible bad future.
And if they all offered an EA Access-like service with as great of a value, I'd persoanlly try it. The money I've saved with EA Access has been pretty enormous. I probably won't buy an EA game ever again (why would I when I can get most for $30 a year, which is probably about what I'd pay for one of them). For a consumer like me that doesn't mind waiting to play the latest games, it's not a big deal.
I know others would disagree with me, and that's great because it's not like games won't still be sold the old traditional way.
Your argument would hold more water if they had stopped selling their games the traditional way and only offered them through their program...but I don't see that happening (and honestly, why would they when they can still sell those games for $60!).
I personally don't see the "threat" to Games with Gold or PS+...there's no way either service would offer the amount of big budget games that EA Access has provided. Sure, it might have an effect, but it's not like we are going from an EA game every month on XBL/PSN to no games upon the arrival of EA Access.