They already do. It's called legal. I've been in this situation numerous times already with PayPal and a few others. They won't even look at the matter until your lawyer sends a nasty letter. At which point they'll look at it. And then either cut you a check or kindly tell you to go fuck yourself, politely.
If legal has to talk to your customers directly, your business is broken. Its an unrecoverable runtime error. Gurus are meditating.
Most companies have teams similar to this, but they are often used wrong, have the wrong type of staff, bad/poor procedures and processes or are under/over-utilized for escalated problems (so too much or too little goes to them).
Additionally, you might be surprised by how difficult it is to find quality staff (especially at the relatively poor salaries often on offer) that has the "right" mindset to be successful for a role like this. The level of customer service, problem resolution skills, knowledge of possible problems & their resolution (without checking a manual, notes, colleagues), quick response and thick skin/hardheadedness for the abuse you will get, when you are trying to help. Sometimes customers are irrational, make mistakes, blame the company for their errors and won't accept it was their error. More often the case (when I did this role), it was a joy to help customers to resolve the problem so they are happy (or happier) with the result.
You need a department that can take responsibility for account lockouts and resolve them! STAT! It is not acceptable for no one in the company to know why an account was disabled or how to go about reinstating it!
If piracy can be called "stealing" and no one bats an eye, I'm going to go ahead and call account lockouts with resolution refusal stealing as well. $1000 is well within the bounds of small claims courts in most jurisdictions.