Here are the FAA's regulations on batteries for those who travel with cordless tools:
https://www.tsa.gov/travel/security-screening/whatcanibring
A large part of the problem is that the TSA morons routinely ignore or are completely unaware of the regs and make up their own on the spot. It's a real crapshoot.
Not to mention the actual regs can change minute-by-minute.
I have quite a lot of titanium in my left leg, and even in the surface scanners I usually get a little extra "attention".
"There's something odd about your left leg."
"Yeah, there's a LOT odd about my left leg."
Usually I just quickly mention it's been broken three times and there's a lot of titanium bracketry in there, and they send me on my way after a few quick pats.
One guy was still very doubtful until I said "Look, I can show you the scars pretty easily. I mean, you've already got my belt..."
For the record, the restrictions on cell phones and other devices are ******** from a technical perspective; they're not going to bring the plane down.
The real reasons the restrictions are important and will remain are because they need people to be paying attention during takeoff and landing and because the devices need to be secured so they don't fly around if things go wrong.
Also, a crowd of idiots stuffed into a metal tube and screaming into their cell phones is a guaranteed recipe for chaos and passenger-on-passenger violence. No one rational wants to fly in a world where we have to deal with that...