If you're implying that EA games don't "just work" because they're EA games, that's false. I had a very unique issue with BF4, and the support I received should have fixed it instantly. Heck, at one point they had escalated it to who they claimed were some DICE devs. Don't know if that just means really high end support team peeps, or if it was actually the devs. Either way it was nice. (If you're interested, I had a very weird registry issue, but long story short it was DELL's fault)
I've contacted Steam for minor things, such as transferring a game from accounts, deleting a game on an account, and an account that acted like it didn't exist.
The first one they refused to do anything, and told me to buy the game again. To contrast with EA, I once bought an EA game (NFS:HP3) via Steam. I put in my wrong origin email, so the game was registered with my wrong account. Contact EA, they IMMEDIATELY gift me a SECOND copy of the game on my main account, NO QUESTIONS ASKED.
I have a family shared account on Steam. The other account owns Arma 3. I could play it just fine originally, but I once tried it for free on a free weekend of the game (as it had disappeared from the other account's library due to it also being in mine). This causes the game to be PERMANENTLY STUCK in my account, so it no longer shows up in the other account. However, it doesn't show up in mine either. I've tried disabling, de-authorizing, etc and starting over, but nothing I can do will fix the issue. Contact Steam, I tell them EXACTLY how they can fix it (remove the game from my library) and they tell me it's a known issue and there's nothing they can do about it. To paraphrase, "Go f*** yourself".
The third time I have contacted their support was regarding an old account (the one from the first story) that refused to allow me to sign in. It had done this for months, and it refused to send me a password reset. Many months pass, and Steam can't even find the account anymore, so I can't even attempt to reset the password. Contact support, give them all the info I have, and they fixed it instantly.
EA's support... NOT just an email type thread of sorts, they have chat and phone options. ALWAYS USE THE PHONE OPTION! YOU WILL GET MUCH BETTER SERVICE THERE! I've also found that the "In Game" department gives better/more knowledgeable representatives. I have LITERALLY talked for an hour and a half AFTER SOLVING MY ISSUE with MULTIPLE reps because they are legitimately nice people, and speak proper English. Roughly over half of the guys I've talked to tend to be this way (and ALL are native English speakers).
I've had 29 different cases on my account with EA, and a few other on my father's. These 29 have been resumed multiple times as well, so it's really not a fair number. These range from very unique/strange issue regarding BF4 as mentioned above (also mentioned how the first couple things they tried would have fixed it, but I had some really strange registry issues), password changes, Battlelog errors, CTE not issuing to my account, promotional items not issuing, billing issues, etc. I've had over 40 or so reps most likely, and I've had two that I can remember who stuck out as bad/poor.
To get back to your comment, EA's games aren't broken, 95% of the time, they do "just work", just like any other games. I've had a bad track history with issues, however I know many friends who also use Origin and the majority of them haven't had issues.