I have never had a problem on more than 20 flights, including Delta, AA and JetBlue, including checked and carryon. Inspire, P2 or P3 batteries were looked at by TSA in checked baggage (they leave a note stating they've inspected the bag) without incident. Never took the Inspire as a carryon, but never had a problem with P2 or P3 batteries as carryon, except one time, a JetBlue flight attendant questioned my DJI labeled back pack and asked what I was carrying. When I told her it was a quad copter she asked to see and objected to 4 batteries. She kept me for 10 min's while she asked around and then let me go.
I am concerned however about these batteries after discovering last week that 3 of my 8 Inspire batteries were visibly swollen and wouldn't fit into the inspire or the case. Hadn't looked at them in 5 months, and needless to say, they wouldn't charge. From now on, I'm packing lipo safety bags both for flights and home storage. Just ordered small travel bags and larger case (for home) from Amazon.