Funny you should say this, because I had a similar experience flying UA out of LAX a few weeks ago. "EZ check-in" said it couldn't give me my boarding pass, and I had to stand in a very long line in order to get checked-in. Thankfully, security line wasn't too bad in my case. LAX T3 security line is usually long, and there was no elite line as of when I last flew.

No particular bad experiences with AS in this regard, but then again, I almost always use web check-in.