It is Boeing designing the aircraft, not the FAA...
In the US, the FAA can only review and validate what has been submitted. It is illegal in the US to design by review.
As noted, the FAA cannot tell Boeing they cannot use LI batteries, if Boeing has submitted all of the required data to show that the issues have been met.
Now, as we can see, the FAA is looking at the Boeing process, from manufacturing down/up, to review if the process and procedures Boeing uses need improvement.
This is not simply about showing Li batteries are safe, this is about Boeing proving their process is safe...