The problem is that it's not quite code. It's almost code, but without the precision, which puts it into a sort of Uncanny Valley of code-ness. It's detailed instructions for someone to write code, but the someone in this case is an alien or insane or on drugs so they might interpret it the way you meant it or they might go off on some weird tangent. You never know, and that means you'll need to check it with almost as much care as you'd take writing it.

Also, having it write its own tests doesn't mean those tests will themselves be correct let alone complete. This is a problem we already have with humans, because any blind spot they had while writing the code will still be present for writing the tests. Who hasn't found a bug in tests, leading to acceptance of broken code and/or rejection of correct alternatives? There's no reason to believe this problem won't also exist with an AI, and they have more blind spots to begin with.