There are converters, but they don't allow natural mouse movement. The movement is relegated to a fixed speed, based on how fast you swipe the mouse. It's not natural at all. It's the same as using the gamepad joystick. You don't get anywhere near the control you're seeking when you're used to kb/mouse.
And I can understand why consoles won't give us that functionality. First off, the obvious advantage goes to kb/mouse over controller. But more importantly, the console is intended for the TV in the family room. And it's hard to control a mouse and keyboard on your lap sitting on the couch. The environment is just not usually suited for kb/mouse. Unless they invent a "breakfast table" that can lean and bend as necessary, and hold your mouse and keyboard even when you let go. And I think there are some things like that out there. But the developers still have to write the code into the games to allow natural mouse movement. Once they do, invest heavily in manufacturers that provide a "console-ready kb/mouse with flexible moving USB table:. That will be every gamer's dream!