No, you certainly are not a graphics expert. I am not either, but at least I know that scenes are not composed and rendered for each pixel. So, when you go from 1080p to 720p which has 2.25 times less pixels, you never get 2.25 times more frame rate. It depends heavily on the game of course but at best you get something less than 2x, while at worse something like a 25% frame rate benefit.
Actually you can get a much higher frame-rate from a small performance boost depending on the game. Generally you have a fixed amount of time to draw a picture, so if you miss the mark by only a little bit, you only need a little bit of extra power to not miss the mark. This is why many modern engines slightly decrease the resolution when they know their drawing is going to come in slightly late.
A console that's twice as powerful, really should be able to have twice the frame rate at the same resolution. BUT, I doubt that's what most developers will choose. The public cares less about 60fps than hardcore gamers think. By increasing the resolution to something above 1080p, the picture will clearly look better on 4K TVs. (Remember: The picture doesn't have to be the full 4K to look better on a 4K TV.) A much sharper, clearer picture at a solid 30 fps is more marketable than the same 1080p picture at 60 fps.