When my Origin account was hacked, I found out that hackers used a very basic vulnerability in Gmail - they've logged into my Origin account, changed the language to Russian, and then changed the password - I received the "your password has been changed" email, but because it was in russian, gmail automatically put it in Spam folder and I never saw it(when I eventually found it the message shown by gmail was "this email is in a different language than used normally for this email address so we've automatically marked it as spam".). Obviously by the time I realized, the "I didn't do this!" link in the email has expired and I had to call EA to recover my account(surprisingly, I did!).
So yeah, now I have 2FA enabled on my origin account, but I still wish I received a text message telling me my password was changed.