Power bottoms like to be in charge while getting fucked up the ass. It's a pretty common gay term for - not quite topping from the bottom, but for a specific sort of demanding sexual partner who knows what they want and will insist on it in bed. It's very explicitly sexual in nature, but niche enough that straights might not get it, which is probably why they used it on their license plate. Good for a giggle. No harm there, more power to them.

But combine reading that with looking at a picture of a kid and dad, and it's kinda gross. Like seeing adds for diapers in your porn feed.

Jesus Christ stop reaching for a prejudice that isn't there you fucking victim fetish. Power bottoming is a pretty explicit term. That's the whole point of getting it on a license plate, to get a giggle about an explicit thing shown off in public.