Thanks for sharing your question with us.  The specific reason why you see that permission is that the feature runs even when you switch to a different tab in Chrome.  For example, you launch Chrome Remote Desktop in a new tab and connect to another computer.  Then you switch to a separate tab (for example, to check your email).  Even though you're not actively using Chrome Remote Desktop at this point, it's still running and active.

But rest assured, Chrome Remote Desktop can only be activated explicitly by two users (one on the host side, one on the client side).  When you stop sharing or close the browser tab, it is completely shut down and no residual components are ever left running.

Hope this helps to answer your question.

Stephen